To determine the half life of radioactive element Barium.

Aims The aim of this experiment is to help students in understanding the half life, average life, nature of radioactivity and isotope generator and the preference of half life over average life.

Objective The objective of this experiment is to determine the half life of Barium-137m.

Equipment G.M counter, Cesium Barium generator, solution of HCl, Stopwatch. Timer Scalar.

Theory

Radioactivity Radioactivity is the process whereby unstable atomic nuclei release energetic subatomic particles. The word radioactivity is also used to refer to the

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subatomic particles themselves. This phenomenon is observed in the heavy elements, like uranium, and unstable isotopes, like carbon-14. Radioactivity was first discovered in 1896 by the French scientist Henri Becquerel, after which the SI unit for radiation, the Becquerel, is named. Becquerel discovered that uranium salts were able to blacken a photographic plate placed in the dark, even through a paper barrier. Subsequent experiments distinguished three distinct types of radiation -- alpha particles, beta particles, and gamma rays. These are positively charged, negatively charged, and neutral, respectively. In many countries, human exposure to radioactivity is measured in rads, where one rad represents 0.01 joule of energy absorbed per kilogram of tissue. Radioactivity is a random process, meaning that it is physically impossible to predict whether or not a given atomic nucleus will decay and emit radiation at any given moment. Rather, radioactivity is quantified using half-life, which is the period of time it takes for half of the given nuclei to decay. Half-life applies to a sample of any size, from a microscopic quantity to all the atoms of that type in the universe. Half-life varies widely, from a couple seconds (Astatine-218) to billions of years (Uranium-238).

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Cesium

Atomic Number:55

Atomic Radius: 265.4 pm

Atomic Symbol: CsMelting Point:

28.5 ºC

Atomic Weight: 132.9054 Boiling Point: 671 ºC

Electron Configuration:

[Xe]6s1Oxidation States:

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The metal is characterized by a spectrum containing two bright lines in the blue (accounting for its name). It is silvery gold, soft, and ductile. It is the most electropositive

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and most alkaline element. Cesium, gallium, and mercury are the only three metals that are liquid at or around room temperature. Cesium reacts explosively with cold water, and reacts with ice at temperatures above -116°C. Cesium hydroxide is a strong base and attacks glass. Cesium reacts with the halogens to form a fluoride, chloride, bromide, and iodide. Cesium metal oxidized rapidly when exposed to the air and can form the dangerous superoxide on its surface.

Applications Cesium is used in industry as a catalyst promoter, boosting the performance of other metal oxides in the capacity and for the hydrogenation of organic compounds. Cesium nitrate is used to make optical glasses. Cesium is sometimes used to remove traces of oxygen from the vacuum tubes and from light bulbs. Cesium salts are used to strength various types of glass. The chloride is used in photoelectric cells, in optical instruments, and in increasing the sensitivity of electron tubes. Cesium is used in atomic clocks and more recently in ion propulsion systems. Cesium in the environment

Although cesium is much less abundant than the other alkali metals, it is still more common than elements like arsenic, iodine and uranium. Few cesium mineral are know, pollucite is the main: they are silicate magmas cooled from granites. World production of cesium compounds is just 20 tones per year, coming mainly from the Bernic lake (Canada) with a little from Zimbabwe and South-West Africa.

Health effects of cesium Humans may be exposed to cesium by breathing, drinking or eating. In air the levels of cesium are generally low, but radioactive cesium has been detected at some level in surface water and in many types of foods.

The amount of cesium in foods and drinks depends upon the emission of radioactive cesium through nuclear power plants, mainly through accidents. These accidents have not occurred since the Chernobyl disaster in 1986. People that work in the nuclear power industry may be exposed to higher levels of cesium, but many precautionary measurements can be taken to prevent this.

It is not very likely that people experience health effects that can be related to cesium itself. When contact with radioactive cesium occurs, which is highly unlikely, a person can experience cell damage due to radiation of the cesium particles. Due to this, effects such as nausea, vomiting, diarrhea and bleeding may occur. When the exposure lasts a long time people may even lose consciousness. Coma or even death may than follow. How serious the effects are depends upon the resistance of individual persons and the duration of exposure and the concentration a person is exposed to.

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Environmental effects of cesium Cesium occurs naturally in the environment mainly from erosion and weathering of rocks and minerals. It is also released into the air, water and soil through mining and milling of ores.Radioactive isotopes of cesium may be released into the air by nuclear power plants and during nuclear accidents and nuclear weapons testing.

The radioactive isotopes can only be decreased in concentration through radioactive decay. Non-radioactive cesium can either be destroyed when it enters the environment or react with other compounds into very specific molecules. Both radioactive and stable cesium act the same way within the bodies of humans and animals chemically.

Cesium in air can travel long distances before settling on earth. In water and soils most cesium compounds are very water-soluble. In soils, however, cesium does not rinse out into the groundwater. It remains within the top layers of soils as it strongly bonds to soil particles and as a result it is not readily available for uptake through plant roots. Radioactive cesium does have a chance of entering plants by falling on leaves.

Animals that are exposed to very high doses of cesium show changes in behaviour, such as increased or decreased activity

Barium

Atomic Number:56 Atomic Radius: 217.3 pm

Atomic Symbol:Ba

Melting Point: 727 ºC

Atomic Weight:137.34

Boiling Point: 1897 ºC

Electron Configuration:

[Xe]6s2 Oxidation States: 2

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Barium is often used in barium-nickel alloys for spark-plug electrodes an in vacuum tubes as drying and oxygen-removing agent. It is also used in fluorescent lamps: impure barium sulfide phosphoresces after exposure to the light. Barium compounds are used by the oil and gas industries to make drilling mud. Drilling mud simplifies drilling through rocks by lubricating the drill.Barium compounds are also used to make paint, bricks, tiles, glass, and rubber. Barium nitrate and chlorate give fireworks a green color.

Barium in the environment Barium is surprisingly abundant in the Earth's crust, being the 14th most abundant element.  High amounts of barium may only be found in soils and in food, such as nuts, seaweed, fish and certain plants. Because of the extensive use of barium in the industries human activities add greatly to the release of barium in the environment. As a result barium concentrations in air, water and soil may be higher than naturally occurring concentrations on many locations.

Barium enters the air during mining processes, refining processes, and during the production of barium compounds. It can also enter the air during coal and oil combustion.The chief mined ores are barite, which is also the most common and witserite. The main mining areas are UK, Italy, Czech Republic, USA and Germany. Each year about 6 million tonnes are produced and reserves are expected to exceed 400 million tonnes.

Health effects of barium The amount of barium that is detected in food and water usually is not high enough to become a health concern. People with the greatest risk to barium exposure with additional health effects are those that work in the barium industry. Most of the health risks that they can undergo are caused by breathing in air that contains barium sulphate or barium carbonate.

Many hazardous waste sites contain certain amounts of barium. People that live near them may be exposed to harmful levels. The exposure will than be caused by breathing dust, eating soil or plants, or drinking water that is polluted with barium. Skin contact may also occur. The health effects of barium depend upon the water-solubility of the compounds. Barium compounds that dissolve in water can be harmful to human health. The uptake of very large amounts of barium that are water-soluble may cause paralyses and in some cases even death.

Small amounts of water-soluble barium may cause a person to experience breathing difficulties, increased blood pressures, heart rhythm changes, stomach irritation, muscle weakness, changes in nerve reflexes, swelling of brains and liver, kidney and heart damage.

Barium has not shown to cause cancer with humans. There is no proof that barium can cause infertility or birth defects.

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Environmental effects of barium Some barium compounds that are released during industrial processes dissolve easily in water and are found in lakes, rivers, and streams. Because of their water-solubility these barium compounds can spread over great distances. When fish and other aquatic organisms absorb the barium compounds, barium will accumulate in their bodies. Because it forms insoluble salts with other common components of the environment, such as carbonate and sulphate, barium is not mobile and poses little risk. Barium compounds that are persistent usually remain in soil surfaces, or in the sediment of water soils. Barium is found in most land soils at low levels. These levels may be higher at hazardous waste sites. Cesium-Barium Generator

This Cs-137/Ba-137 m Isotope Generator is used to demonstrate the properties of radioactive decay. Based on the original Union Carbide patented design, it offers exceptional performance, ease-of-use and safe operation.

Each generator contains 10 µCi of Cs-137, which represents one Exempt Quantity, making it free from specific State and Federal licensing. The generator can produce up to 1000 small aliquots of the short-lived Ba-137m isotope with a half-life of 2.6 minutes.

Each generator is supplied with 250 mL of eluting solution (0.9% NaCl in 0.04M HCl). The parent isotope Cs-137 with a half-life of 30.1 years beta decays (94.6%) to the metastable state of Ba-137m. This further decays by gamma emission (662 keV) with a half-life of 2.6 min. to the stable Ba-137 element. During elution, the Ba-137m is selectively "milked" from the generator, leaving behind the Cs-137 parent. Regeneration of the Ba-137m occurs as the Cs-137 continues to decay, re-establishing equilibrium in

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less than 1 hour.

Approximately 30 minutes after elution, the residual activity of the Ba-137m sample has decayed to less than one thousandth of its initial activity, making it safe for disposal. When used with the eluting solution supplied, bleed through of the parent Cs-137 is less than 50 Bq/mL, affording a long working life. Each kit is supplied with the generator, syringe, tube, 250 mL of solution and a storage case.

Half Life The half-life of a quantity whose value decreases with time is the interval required for the quantity to decay to half of its initial value. The concept originated in describing how long it takes atoms to undergo radioactive decay, but also applies in a wide variety of other situations.The term "half-life" dates to 1907. The original term was "half-life period", but that was shortened to "half-life" starting in the early 1950s.Half-lives are very often used to describe quantities undergoing exponential decay—for example radioactive decay—where the half-life is constant over the whole life of the

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decay. However, a half-life can also be defined for non-exponential decay processes, although in these cases the half-life varies throughout the decay process. For a general introduction and description of exponential decay, see the article exponential decay. For a general introduction and description of non-exponential decay, see the article rate law.The table shows the reduction of the quantity in terms of the number of half-lives elapsed.

Probabilistic nature of half-life A half-life often describes the decay of discrete entities, such as radioactive atoms. In that case, it does not work to use the definition "half-life is the time required for exactly half of the entities to decay". For example, if there is just one radioactive atom with a half-life of 1 second, there will not be "half of an atom" left after 1 second. There will be either zero atoms left or one atom left, depending on whether or not the atom happens to decay.Instead, the half-life is defined in terms of probability. It is the time when the expected value of the number of entities that have decayed is equal to half the original number. For example, one can start with a single radioactive atom, wait its half-life, and measure whether or not it decays in that period of time. Perhaps it will and perhaps it will not. But if this experiment is repeated again and again, it will be seen that it decays within the half life 50% of the time.In some experiments (such as the synthesis of a superheavy element), there is in fact only one radioactive atom produced at a time, with its lifetime individually measured. In this case, statistical analysis is required to infer the half-life. In other cases, a very large number of identical radioactive atoms decay in the time-range measured. In this case, the central limit theorem ensures that the number of atoms that actually decay is essentially equal to the number of atoms that are expected to decay. In other words, with a large enough number of decaying atoms, the probabilistic aspects of the process can be ignored.There are various simple exercises that demonstrate probabilistic decay, for example involving flipping coins or running a computer program.

The radioactive half-life for a given radioisotope is the time for half the radioactive nuclei in any sample to undergo radioactive decay. After two half-lives, there will be one fourth the original sample, after three half-lives one eight the original sample, and so forth.

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The radioactive half-life gives a pattern of reduction to half in any successive half-life period.

Formulae for half-life in exponential decay A quantity is said to be subject to exponential decay if it decreases at a rate proportional to its value. Symbolically, this can be expressed as the following differential equation, where N is the quantity and λ is a positive number called the decay constant.

The solution to this equation is:

Here N(t) is the quantity at time t, and N0 = N(0) is the initial quantity,

An exponential decay process can be described by any of the following three equivalent formulae:

Nt = N0e − t / τ

Nt = N0e − λt

where

N0 is the initial quantity of the thing that will decay (this quantity may be measured in grams, moles, number of atoms, etc.),

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Nt is the quantity that still remains and has not yet decayed after a time t, t1 / 2 is the half-life of the decaying quantity, τ is a positive number called the mean lifetime of the decaying quantity, λ is a positive number called the decay constant of the decaying quantity.

The three parameters t1 / 2, τ, and λ are all directly related in the following way:

where ln(2) is the natural logarithm of 2 (approximately 0.693).By plugging in and manipulating these relationships, we get all of the following equivalent descriptions of exponential decay, in terms of the half-life:

Regardless of how it's written, we can plug into the formula to get

Nt = N0 at t=0 (as expected—this is the definition of "initial quantity") Nt = (1 / 2)N0 at t = t1 / 2 (as expected—this is the definition of half-life) Nt approaches zero when t approaches infinity (as expected—the longer we wait,

the less remains).

Half-life in non-exponential decay Many quantities decay in a way not described by exponential decay—for example, the evaporation of water from a puddle, or (often) the chemical reaction of a molecule. In this case, the half-life is defined the same way as before: The time elapsed before half of the original quantity has decayed. However, unlike in an exponential decay, the half-life depends on the initial quantity, and changes over time as the quantity decays.As an example, the radioactive decay of carbon-14 is exponential with a half-life of 5730 years. If you have a quantity of carbon-14, half of it (on average) will have decayed after 5730 years, regardless of how big or small the original quantity was. If you wait another 5730 years, one-quarter of the original will remain. On the other hand, the time it will take a puddle to half-evaporate depends on how deep the puddle is. Perhaps a puddle of a certain size will evaporate down to half its original volume in one day. But if you wait a second day, there is no reason to expect that precisely one-quarter of the puddle will remain; in fact, it will probably be much less than that. This is an example where the half-life reduces as time goes on. (In other non-exponential decays, it can increase instead.)For specific, quantitative examples of half-lives in non-exponential decays, see the article Rate equation.A biological half-life is also a type of half-life associated with a non-exponential decay, namely the decay of the activity of a drug or other substance after it is introduced into the body.

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Mean lifetime

If the decaying quantity is the number of discrete elements of a set, it is possible to compute the average length of time for which an element remains in the set. This is called the mean lifetime (or simply the lifetime) and it can be shown that it relates to the decay rate,

The mean lifetime (also called the exponential time constant) is thus seen to be a simple "scaling time":

Thus, it is the time needed for the assembly to be reduced by a factor of e.A very similar equation has shown above, which arises when the base of the exponential is chosen to be 2, rather than e. In that case the scaling time is the "half-life"

Methodology First prepare a solution of Cs-Ba by using the mini generator. fill your syringe with eluting solution. Remove the stoppers on either end of the mini-generator column.

Hold the mini-generator carefully above the glass vial with the arrows on the mini-generator pointing downward. While your partner holds the glass vial, insert the syringe firmly into the hole on the top of the generator without pushing on the syringe plunger. While carefully holding the mini-generator and the vial, use the syringe to force about 10 drops (1 mL) of solution into the mini-generator. DO NOT SUCK UP ON THE SYRINGE; ONLY INSERT SOLUTION IN THE DIRECTION OF THE ARROWS ON THE MINI-GENERATOR. This will release the barium 137m into the glass vial. Once you’ve pushed the solution through, remove the syringe and place it and the mini-generator carefully back on the table.

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Place the sensor window of the Geiger counter directly next to the glass vial and you will hear an increase in the level of radiation, this is the radioactive decay of barium 137m into barium 137.Repeat this at least 15 times and record all of your data on your table for a total of at least 15 data points.Turn the Geiger counter off. Replace the stoppers on the two ends of the mini-generator and return any remaining eluting solution from your syringe into the bottle from which you removed it. Pour the contents of your glass vial into the HCl waste bottles, replace the cover on the glass vial and leave it with the “dirty vials.”

Observations and Calculations

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Sr. # Time(min) Activity(Cpm)1 1 9352 2 7453 3 5344 4 4525 5 3596 6 2917 7 2508 8 1939 9 20410 10 16011 11 15712 12 13013 13 13214 14 10915 15 110

Now using these readings I draw a graph and from that graph I calculated the half life of Barium metastable. For determining the half-life of Ba-137 take the activity at any time from the graph and divide this activity by two. Note that the time duration between these two activities is the half-life of Barium metastable.

Activity = 935 Cpm

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Time , = 1 min.Half of the activity = 467.5 Cpm

Time , = 3.6 min.

Half Life of Barium metastable = = 3.6 - 1= 2.6 min.Actual Half life of Barium = 2.551 min.

% error =

% error =

% error = 1.9 %

Precautions and Sources of Errors Lab uses a sealed radioactive source. Within this mini-generator is radioactive cesium with a half-life of about 30 years. Because this source is sealed, you will not come into contact with this cesium unless the mini-generator is broken. Therefore, please be careful handling this piece of equipment. The radioactive barium that you will be working with today has a very short half-life. By the time the lab is over today, more than 10 half-lives will have passed, at which point the radioactivity levels are equal to the background radioactivity normally present in the air. Therefore, this radioactive source is very safe to work with AS LONG AS THE FOLLOWING SAFETY

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No food or drinks are allowed in this lab; leave all food outside the lab room.

Smoking is never allowed in the lab.

Do not apply cosmetics during this lab session.

Safety goggles and gloves must be worn at all times when working with the radioisotope generators.

You must wear closed-toe shoes; no sandals may be worn.

The eluting solution contains a weak concentration of HCl, this can cause burns on your skin and clothing, please be careful to not spill it and wear gloves and goggles at all times.

Notify your lab instructor of any spills or accidents immediately.

Please do not touch the sensor window face plate on the Geiger counter; this can ruin this expensive piece of equipment.

Dispose of your used gloves in the trash and wash your hands thoroughly before leaving the lab.

Do not gather near the G.M counter otherwise it will not give you correct readings.

Quickly take the readings because it Ba-137m have a very short life.

Be careful with the radiations because Beta radiations are very dangerous.

Discussion All nuclei heavier than lead (and many isotopes of lighter nuclei) have a finite probability of decaying spontaneously into another nucleus plus one or more lighter particles. One of the decay products may be an alpha-particle (two protons and two neutrons--the stable nucleus of a helium atom). Alternatively, a nucleus with more neutrons than it can maintain in stability may decay by emission of an electron from the nucleus (beta-decay) which corresponds to the conversion of a neutron to a proton. These electrons may emerge with a kinetic energy of up to several MeV.After alpha or

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beta decay, the residual nucleus may be left in an excited state. In this case, a transition to a state of lower energy of the same nucleus will occur almost immediately with the emission of a photon (gamma ray). The spectrum of photons emitted from the various excited states of a nucleus will have discrete frequencies n, corresponding to transitions E = h , between discrete energy levels of the nucleus. The gamma ray spectrum from an excited nucleus is thus analogous to the line spectrum of visible radiation from an atom due to excited electrons, with the notable difference that the MeV energy changes of the nucleus are 6approximately 10 times as large as energy changes in transitions between atomic states (where E atomic several eV). In early experiments on beta-decay, it was observed that each decay was not a simple one in which an electron and the recoil nucleus came off with equal and opposite momentum. The electrons, in fact, were emitted with a continuous spectrum of energies . It was subsequently suggested by Pauli and Fermi that in each decay, another particle of zero mass and charge, called the neutrino, was emitted. Experimental verification of the neutrino has been obtained by observation of its rare interaction with matter.

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Questions and Answers Why is this experiment on half-life being presented?The purpose of this experiment is to explain the process of radioactive decay and its relationship to the concept of half-life. The primary intent is to demonstrate how the half-life of a radionuclide can be used in practical ways to "fingerprint" radioactive materials, to "date" organic materials, to estimate the age of the earth, and to optimize the medical benefits of radionuclide usage.

What is meant by the "decay" of a radionuclide?A radionuclide represents an element with a particular combination of protons and neutrons (nucleons) in the nucleus of the atom. A radionuclide has an unstable

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combination of nucleons and emits radiation in the process of regaining stability. Reaching stability involves the process of radioactive decay. A decay, also known as a disintegration of a radioactive nuclide, entails a change from an unstable combination of neutrons and protons in the nucleus to a stable (or more stable) combination. The type of decay determines whether the ratio of neutrons to protons will increase or decrease to reach a more stable configuration. It also determines the type of radiation emitted.

How do radioactive atoms decay?Radioactive atoms decay principally by alpha decay, negative beta emission, positron emission, and electron capture.

How does the neutron-to-proton number change for each of these decay types?Alpha decay typically occurs in nuclei that are so big that they can't be stable. In alpha decay, the nucleus ejects a helium nucleus (alpha particle) composed of two neutrons and two protons, dropping the mass of the original nucleus by four mass units. This smaller nucleus is easier to keep in a stable form.

Beta decay?In negative beta decay, the nucleus contains an excess of neutrons. To correct this unstable condition, a neutron is converted into a proton, which keeps the nucleus the same size (i.e., the same atomic mass) but increases the number of protons (and therefore the atomic number) by one. In the process of this conversion, a beta particle with a negative charge is then ejected from the nucleus.

What about positron decay?In positron decay, the opposite situation occurs: the proton to neutron ratio is greater than desired. Accordingly, a proton is converted into a neutron and a beta particle (but with a positive charge!) is ejected.Again, the nucleus remains the same size, but the number of protons decreases by one.

And electron capture?Electron capture results in the same outcome as positron decay in that, in this process, the nucleus stays the same size and the number of protons decreases by one. In this type of decay, however, the nucleus captures an electron and combines it with a proton to create a neutron. X-rays are given off as other electrons surrounding the nucleus move around to account for the one that was lost.

Each one of these decay types may also involve the release of one or more photons of gamma radiation. These photons are pure energy given off by the nucleus in its process of achieving stability.

Does anything else occur during the decay process?You may have noticed that the decay modes involve particles. Therefore, decay of a radionuclide results in a loss of mass. The mass is converted into energy and released.

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Is it possible to predict when a given radioactive atom will decay?No, its not. The decay of an individual atom is a random event. However, it is possible to predict when decay will occur based on probability, particularly when there are a lot of radioactive atoms around. Fortunately, since atoms are so small, it doesn't take much radioactive material to represent a lot of atoms.

What is meant by the decay rate?The decay rate is simply the number of radioactive atom decays occurring over a specified time.

Is there another designation for the decay rate?Yes. The decay rate is conventionally known as the "activity" or "radioactivity" of a material, sample or medium.

What kinds of units are used to reflect activity or decay rate?Units of activity include disintegration per second (dps), disintegration per minute (dpm), the curie (Ci), and the becquerel (Bq). Each of these units is a measure of the number of atoms occurring over a specified time. A curie of activity, for example, represents 37 billion atoms decaying every second (37 billion dps) - a very large number! - while one (1) becquerel is equivalent to a single atom decaying each second.

What factors can be used to characterize or "fingerprint" a radionuclide?There are basically three factors that separate one radionuclide from another. These are its half-life, the particulate or photon energy associated with its decay, and the type of emission

What do you mean by half-life?A half-life is defined as the amount of time required for one-half or 50% of the radioactive atoms to undergo a radioactive decay. This is also known as the "radioactive" or "physical" half-life. Every radioactive element has a specific half-life associated with it.

Since the half-life is defined for the time at which 50% of the atoms have decayed, why can't we predict when a particular atom of that element will decay?The concept of half-life relies on a lot of radioactive atoms being present. As an example, imagine you could see inside a bag of popcorn as you heat it inside your microwave oven. While you could not predict when (or if) a particular kernel would "pop," you would observe that after 2-3 minutes, all the kernels that were going to pop had in fact done so. In a similar way, we know that, when dealing with a lot of radioactive atoms, we can accurately predict when one-half of them have decayed, even if we do not know the exact time that a particular atom will do so.

What else can you tell me about the half life of atoms?Half-lives range from fractions of a second to billions of years. For example, Carbon-14 (C-14), a naturally occurring radionuclide, has a half-life of 5,730 years. After this amount of time passes, half of the initial amount of C-14 is present. Therefore, if you

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began with two (2) curies of C-14, one-half of that amount, or one curie, would be present 5,730 years later. After two (2) half-lives, one-fourth of the initial activity, or 0.5 curies, would be left. After three (3) half-lives, which is more than 17,000 years later, one-eighth of the original C-14 activity, or 0.25 curies, would remain, and so forth.

Well, 5,730 years seems like a long time to wait for the original C-14 activity to diminish by 50%. You're right. This points out the fact that the rate of decay of short-lived materials is much faster than for their long-lived counterparts.

Can I make the process hurry along?Unfortunately, no. Each radionuclide has its own characteristic half-life. No operation or process of any kind (i.e., chemical or physical) has ever been shown to change the rate at which a radionuclide decays.

Where can I find a listing of half lives of various radionuclides?Values for individual half-lives can be found in the literature. This includes health physics textbooks and the Chart of the Nuclides, a copy of which appears in the "Links" section of the IEM web page (red button on the left), under the category entitled "Gadgets and Tools".  In addition, the "Tool Box" section of the IEM web page contains a listing of half-lives for commonly-encountered radionuclides, in order by element name.

What is meant by the term specific activity?The term "specific activity" refers to the activity of a particular radioactive element (i.e., the number of decays per time) divided by the mass of material in which it exists. Put another way, the specific activity defines the relationship between the activity and the mass of material. Units for specific activity include the curie per gram (Ci/g) and the becquerel per kilogram (Bq/kg), etc.

How is specific activity related to half-life?Half-life has a profound effect on the specific activity. The shorter the half-life, the higher the specific activity. As a short-lived radionuclide undergoes the process of radioactive decay, atoms of the radionuclide in question emit radioactivity (alpha particles, beta particles, etc.) frequently as they decay. The higher this rate of decay (activity) while maintaining a (nearly) constant mass, the higher the specific activity. On the other hand, atoms of a long-lived radionuclide (one with a long half-life) do not decay nearly as frequently. Therefore, a lower rate of decay within a specified mass of material results in a lower specific activity.

What are some examples of radionuclides with low specific activities? Many radionuclides have half-lives of millions to billions of years. Uranium-238 (U-238), a naturally occurring radionuclide, has a half-life of 4.5 billion years. Potassium-40 (K-40), another naturally occurring radionuclide found in the air, water, soil (and therefore in foodstuffs and consequently in our bodies), has a half-life of approximately 1.3 billion years. Plutonium-239 (Pu-239), a man-made element, has a half-life of only 240,000 years. Because of their long half-lives, each of these radionuclides, and many

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others like them, do not decay into other elements on a very frequent basis. For this reason, their specific activities are considered to be low.

What about high specific activities?Radionuclides with high specific activities must have short half-lives (seconds, minutes, hours, or, at the most, a few years). Many radionuclides have short half lives. For example, Nitrogen-16 (N-16), a radionuclide associated with nuclear power plant operations, has a half-life on the order of seven (7) seconds. Talk about a high rate of decay!

Are there other examples?The metastable form of Technetium-99 (Tc-99m) and Iodine-131 (I-131), both used in nuclear medicine procedures, have half-lives of only six (6) hours and eight (8) days, respectively. Tritium (Hydrogen-3 or H-3), a radioactive isotope of hydrogen and one that is produced both naturally and for man-made purposes, has a half-life of 12.3 years. These radionuclides with short (or relatively short) half-lives decay on a much more frequent basis than their longer half-life counterparts. When each of their respective activities is divided by the same mass (a gram of material, for example), a high specific activity results.

So half-life and mass have some sort of a relationship?Yes. To put this concept in a slightly different perspective, take the case of the two radionuclides Sulfur-35 (S-35) and Phosphorus-32 (P-32). S-35 and P-32 have half-lives of 87 days and 14.3 days, respectively. Therefore, the P-32 decays approximately six (6) times faster than the sulfur. On a mass basis, then, one-sixth (1/6) of a gram of P-32 is essentially equivalent to one (1) gram of S-35 in terms of radioactivity!

Where can I find a list of the specific activities of the various radionuclides?The best place to start is the IEM "Tool Box" (on the left), under the section entitled "Specific Activities". You'll find a pretty comprehensive listing there.

Can an element's half life be used to distinguish it from other elements?Yes, in many cases it can. Successful radionuclide identification is largely determined by the three factors noted previously (half-life, energy, and type of decay). Since many radionuclides have unique half-lives, the half-life can be used for identification purposes. For example, if a sample containing an unknown radionuclide is counted using an appropriate radiation detector, and the observed activity decreases by one-half of the initial activity after fourteen (14) days, the radionuclide is likely P-32, a pure beta emitter (it only decays by beta emission) with a half-life of 14.3 days.

Are there times when this doesn't work?Yes. Some radionuclides do have similar half-lives which would complicate the identification process. However, in these cases, the energies of the radiations they emit during the decay process will differ and can be used to establish the radionuclide's identity.

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How can the concept of half-life be used to determine the age of organic materials?Radiometric dating is a widely used technique that utilizes the half-life of radioactive elements as a means to estimate the age of various materials. Several approaches are used. Perhaps the most widely publicized has been radiocarbon dating.

Tell me more about radiometric dating. In the early 19th century, only a relative time scale (versus an absolute scale) could be used by geologists. They could not determine the absolute amount of time a rock or fossil had been in existence because they had no way to measure their ages. Then, in 1905, less than 10 years after radioactivity was discovered by Henri Becquerel, radiometric dating, using the principle of radioactive decay to measure the age of rocks and minerals, was introduced.

Sounds impressive!Considering that isotopes and decay rates were not known at this time is certainly cause for amazement about these early studies!

So how does radiometric dating work?Radiometric dating relies on the use of radioactive elements as "geological clocks". Since each element decays at its own characteristic rate, geologists can estimate the length of time over which the decays have occurred by measuring the amount of the radioactive parent present relative to the amount of the stable daughter. Put another way, the ratio of parent to daughter can tell us the number of half-lives, which in turn, can be used to find the age in years. As an example, if an equal number of parent and daughter atoms exist, then one-half life has passed.

How does radiocarbon dating work?Carbon-14 (C-14), a radioactive isotope of carbon, is naturally produced in the upper atmosphere through bombardment of Nitrogen-14 (N-14) with cosmic rays. The C-14 is then rapidly oxidized to radioactive carbon dioxide gas which is absorbed and used by plants. This serves as its introduction into the food chain.

Then what?Radiocarbon dating relies on the assumption that C-14 exists in an "equilibrium" concentration in the carbon of living biological materials, meaning the ratio of C-14 in the body to that of stable Carbon, or C-12, stays constant. When a plant or animal dies, it ceases breathing, eating, and/or absorbing carbon (and therefore C-14). Thus, the C-14-to-C-12 ratio is no longer fixed. The C-14 begins to decay back into N-14, resulting in a decrease in the C-14 concentration based on its half-life (a 50% reduction every 5,730 years). Since the rate of decay is known, the concentration (specific activity) of C-14 in organic (carbon-containing) materials can be measured and used to calculate the date that the plant or animal died.

Wow. Does it work all the time?Yes, but only on materials that contain carbon , and only on materials that were once living.

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Where is C-14 dating used?Radiocarbon dating has been used to determine the age of certain fossilized bones. In addition, this technique has been applied with great success in archaeological dating and dating associated with the ice ages.

Are there any shortcomings of this method? Yes. The C-14-to-C-12 ratio has not remained constant with time as determined by measuring the levels of radiocarbon in tree rings. The fact that C-14 is also produced through man-made activities is another confounding factor. With the beginning of the industrial age, large quantities of coal have been burned. Coal is very old, meaning that the ratio of C-14 to C-12 is essentially nonexistent. This has the effect of diluting the ratio in the atmosphere following carbon dioxide releases. Without making a series of corrections to account for these confounding factors, the resulting C-14 age determination will be in error.

Any other limitations?Just one. It has also been stated that this method can only be used on materials less than 50,000-70,000 years old. Beyond that point, there are so few C-14 atoms remaining in the sample that it becomes difficult to measure them.

Can you provide other examples of radiometric dating?Certainly. Potassium-Argon dating is another form. It relies on the decay of Potassium-40 (K-40), a naturally occurring radionuclide, to Argon- 40 (Ar-40), to place an age on rocks and sediments. This method was used recently to estimate the age at which the eruption of the volcano, Vesuvius, occurred in the ancient Roman city of Pompeii. (Historians place the eruption around 79 A.D. or 1,919 years ago, while potassium-argon dating estimated this event occurred 1,926 years ago, an error of less than one percent , but an error nonetheless!)

Are there other types?Rubidium-strontium dating, which relies on the decay of Rubidium-87 to Strontium-87, has been used to date very old terrestrial rocks as well as lunar samples. Thorium-230 (Th-230) has been utilized to date oceanic sediments that are older than the useful range of radiocarbon techniques. The fission-track method relies on the paths, or tracks, produced by charged particles traversing a mineral's crystal lattice as a result of spontaneous fission by uranium impurities.

Anything more?Yes indeed! There are still other interesting methods used in age-dating. One of these is known as thermoluminescence.

What is thermoluminescence and how has it been used?Taken separately, the word "thermo" implies heating, while the word "luminescence" refers to light. In brief, a thermoluminescent material stores radiation energy once it is absorbed. Upon heating the material, this "trapped" energy is released and emits light. The amount of light can be related to the radiation dose received over time or, for the

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purposes of this chapter, to the age of the material if the half-life is known (to account for radioactive decay over periods of up to hundreds of thousands of years).

Can you provide an example?Yes. Following the atomic bomb blasts in Hiroshima and Nagasaki Japan, samples of ceramic roofing tiles, ornamental tiles and brick from various locations within one (1) kilometer (km) of ground zero were collected, broken down into much smaller fragments, and heated. The amount of light released was used as a measure of the radiation dose at the location from which the samples were taken. These doses can then be assigned to the survivors based on where they were when the bombs were dropped.

Why are radionuclides with short half-lives used most often in medical applications?Medical procedures are designed, of course, to help the patient. When certain procedures are performed utilizing radioactivity, it is advantageous and important from a health perspective to use radionuclides that satisfy the desired diagnostic or treatment objective and then decay away before they expose the patient to unnecessary amounts of radiation.

Can you give me an example?Radionuclides such as Tc-99m, with a half-life of six (6) hours, are routinely used in bone scans because the medical objective is successfully reached while the amount of radioactivity diminishes rapidly. Another example is the treatment for thyroid disorders that utilizes I-131 with a short half-life of eight (8) days. Many other examples with this same objective in mind are used in the medical field.

Are long-lived radionuclides ever used in medical applications?Yes. There are cases where using short-lived materials will simply not accomplish the desired medical objective. A classic example involves the use of Pu-238 as the power supply in cardiac (heart) pacemakers. This radionuclide has a pretty long half-life (87.7 years) and a relatively high specific activity - two worthwhile attributes for this application. It is inserted into the battery as a sealed source in the patient to provide power to the pacemaker. Using a sealed source means that the radioactive material stays where it was put. It is readily apparent that using shorter-lived radionuclides for this purpose would not be advantageous because the sources would have to be replaced on a routine basis. And every replacement source is another surgery!

Is Pu-238 used in non-medical applications?Yes, Pu-238 is used as a power source in space missions, such as the relatively recent NASA Galileo launch. The energy associated with the decay of this radionuclide is converted into electricity to power the probe to its desired destination. NASA used this type of power supply because the probe would be traveling so far from the Sun that solar power couldn't be used. As with the medical applications discussed previously, the half-life and associated specific activity merits its use in this application.

I've heard the term "biological half life" before.  Is it different from the physical half-life we have been discussing?Most definitely. In contrast to the radiological (physical) half-life, the biological half-life

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is a measure of how long it takes to eliminate half of the radioactivity taken into the body by biological processes (e.g., excretion).

Can you give me an example?Be glad to. Cesium-137 (Cs- 137) has a physical half-life of approximately 30 years. Left outside the body, half of the initial radioactivity will decay or disappear in that time frame. Inside the body, however, Cs-137 has a biological half-life of only seventy (70) days. This means that biological processes significantly accelerate the rate of clearance associated with this radionuclide in comparison to the radiological half-life. Half of the radioactivity will be gone after 70 days, another half of the radioactivity in another 70 days, etc.

What is an effective half-life?If radioactivity is taken into the body, decay of the radionuclide will occur by both physical and biological means. The effective half-life is a measure of the combined influences of these two distinct half-lives. In the case of the Cs-137 example, the radiological and biological half-lives are thirty (30) years and seventy (70) days, respectively. The effective half-life in this instance is slightly less than seventy (70) days. It is important to note that the effective half-life is always lower than either the biological or the physical half life.

How big is a curie?

A curie is defined as 37 billion disintegrations per second. The curie was originally a comparison of the activity of a sample to the activity of one gram of radium, which at the time was measured as 37 billion disintegrations per second. A radioactive sample that has an activity of 74 billion disintegrations per second, has an activity of 2 curies. When more accurate techniques measured a slightly different activity for radium, the reference to radium was dropped.

Who discovered beta particles?

Henri Becquerel is credited with the discovery of beta particles. In 1900, he showed that beta particles were identical to electrons, which had recently been discovered by Joseph John Thompson.

What are the properties of beta particles?

Beta particles have an electrical charge of -1. Beta particles have a mass of 549 millionths of one atomic mass unit, or AMU, which is about 1/2000 of the mass of a proton or

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neutron. The speed of individual beta particles depends on how much energy they have, and varies over a wide range. It is their excess energy, in the form of speed, that causes harm to living cells. When transferred, this energy can break chemical bonds and form ions.

What conditions lead to beta particle emission?

Beta particle emission occurs when the ratio of neutrons to protons in the nucleus is too high. In this case, an excess neutron transforms into a proton and an electron. The proton stays in the nucleus and the electron is ejected energetically.

This process decreases the number of neutrons by one and increases the number of protons by one. Since the number of protons in the nucleus of an atom determines the element, the conversion of a neutron to a proton actually changes the radionuclide to a different element.

Often, gamma ray emission accompanies the emission of a beta particle. When the beta particle ejection doesn't rid the nucleus of the extra energy, the nucleus releases the remaining excess energy in the form of a gamma photon.

The decay of technetium-99, which has too many neutrons to be stable, is an example of beta decay. A neutron in the nucleus converts to a proton and a beta particle. The nucleus ejects the beta particle and some gamma radiation. The new atom retains the same mass number, but the number of protons increases to 44. The atom is now a ruthenium atom.

Other examples of beta emitters are phosphorous-32, tritium (H-3), carbon-14, strontium-90, and lead-210.

Which radionuclides are beta emitters?

There are many beta emitters. You can find fact sheets for several of them at the Radionuclides page:

tritium cobalt-60 strontium-90 technetium-99 iodine-129 and -131 cesium-137

How do we use beta emitters?

Beta emitters have many uses, especially in medical diagnosis, imaging, and treatment:

Iodine-131 is used to treat thyroid disorders, such as cancer and graves disease (a type of hyperthyroidism)

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Phosphorus-32 is used in molecular biology and genetics research. Strontium-90 is used as a radioactive tracer in medical and agricultural studies. Tritium is used for life science and drug metabolism studies to ensure the safety

of potential new drugs. It is also used for luminous aircraft and commercial exit signs, for luminous dials, gauges and wrist watches.

Carbon-14 is a very reliable tool in dating of organic matter up to 30,000 years old.

Beta emitters are also used in a variety of industrial instruments, such as industrial thickness gauges, using their weak penetrating power to measure very thin materials.

What happens to beta particles in the environment?

Beta particles travel several feet in open air and are easily stopped by solid materials. When a beta particle has lost its energy, it is like any other loose electron. Whether in the outdoor environment or in the body, these electrons are then picked up by a positive ion.

How are people exposed to beta particles?

There are both natural and man-made beta emitting radionuclides. Potassium-40 and carbon-14 are weak beta emitters that are found naturally in our bodies. Some decay products of radon emit beta particles, but its alpha-emitting decay products pose a much greater health risk.

Beta emitters that eject energetic particles can pose a significant health concern. Their use requires special consideration of both benefits and potential, harmful effects.

Key beta emitters used in medical imaging, diagnostic and treatment procedures are phosphorus-32, and iodine-131. For example, people who have taken radioactive iodine will emit beta particles. They must follow strict procedures to protect family members from exposure.

Radioactive iodine may enter the environment during a nuclear reactor accident and find its way into the food chain.

Industrial gauges and instruments containing concentrated beta-emitting radiation sources can be lost, stolen, or abandoned. If these instruments then enter the scrap metal market, or someone finds one, the sources they contain can expose people to beta emitters.

Does the way a person is exposed to beta particles matter?

Yes. Direct exposure to beta particles is a hazard, because emissions from strong sources can redden or even burn the skin. However, emissions from inhaled or ingested beta particle emitters are the greatest concern. Beta particles released directly to living tissue can cause damage at the molecular level, which can disrupt cell function. Because they are much smaller and have less charge than alpha particles, beta particles generally travel further into tissues. As a result, the cellular damage is more dispersed.

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How can beta particles affect people's health?

Beta radiation can cause both acute and chronic health effects. Acute exposures are uncommon. Contact with a strong beta source from an abandoned industrial instrument is the type of circumstance in which acute exposure could occur. Chronic effects are much more common.

Chronic effects result from fairly low-level exposures over a along period of time. They develop relatively slowly (5 to 30 years for example). The main chronic health effect from radiation is cancer. When taken internally beta emitters can cause tissue damage and increase the risk of cancer. The risk of cancer increases with increasing dose.

Some beta-emitters, such as carbon-14, distribute widely throughout the body. Others accumulate in specific organs and cause chronic exposures:

Iodine-131 concentrates heavily in the thyroid gland. It increases the risk of thyroid cancer and other disorders.

Strontium-90 accumulates in bone and teeth.

Is there a medical test to determine exposure to beta particles?

There are tests which can detect the presence of beta-emitting radionuclides in the body, however, special equipment is required and testing is generally done by specialized laboratories and facilities, or such testing is associated with a specific medical procedure in a hospital.

How do I know I'm near beta emitters and beta particles?

You cannot tell if you are being exposed to beta radiation. You cannot see, or feel radiation hitting your body. Specialized equipment is required to determine if you are near a beta radiation source. However, you should be familiar with the radiation warning symbols such as the trefoil shown at right, which indicate that radioactivity is present.

You can protect yourself by avoiding devices with this symbol, and not entering areas where this symbol or others are posted.

How do I protect myself and my family from beta particles?

While very unlikely, you or a member of your family may encounter an industrial instrument or device containing a radioactive source. Every year, hundreds of devices containing radiation sources are lost, stolen, or otherwise drop out of the system for tracking them. For example, a factory that has gone out of business may contain one or more such devices. As the building structure is being dismantled, these forgotten devices often are considered as scrap metal, or someone may think they have value and try to sell them.

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You should avoid these devices. They may bear the radiation warning symbol, a trefoil, as shown above. They may also bear identifying information such as "Nuclear Regulatory Commission" or the name of a radionuclide. If you find a device you think may be radioactive, promptly call your state radiation control office or the hotline for reporting unwanted radioactive material.

To study the Radioactive equilibrium for Barium137m.

Aims The aim of this experiment is to make students familiar in a true sense with the radioactive equilibrium, its types i.e. Secular and Transient Equilibrium. Also to make the students familiar with the concept of decay and growth rate of radioactive elements.

Objective The objective of this experiment is to determine the type of equilibrium forBarium-137.

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Equipment G.M counter, Cesium Barium generator, solution of HCl, Stopwatch. Timer Scalar.

Theory Half Life The half-life of a quantity whose value decreases with time is the interval required for the quantity to decay to half of its initial value. The concept originated in describing how long it takes atoms to undergo radioactive decay, but also applies in a wide variety of other situations.The term "half-life" dates to 1907. The original term was "half-life period", but that was shortened to "half-life" starting in the early 1950s.Half-lives are very often used to describe quantities undergoing exponential decay—for example radioactive decay—where the half-life is constant over the whole life of the decay. However, a half-life can also be defined for non-exponential decay processes, although in these cases the half-life varies throughout the decay process. For a general introduction and description of exponential decay, see the article exponential decay. For a general introduction and description of non-exponential decay, see the article rate law.The table shows the reduction of the quantity in terms of the number of half-lives elapsed.

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Probabilistic nature of half-life A half-life often describes the decay of discrete entities, such as radioactive atoms. In that case, it does not work to use the definition "half-life is the time required for exactly half of the entities to decay". For example, if there is just one radioactive atom with a half-life of 1 second, there will not be "half of an atom" left after 1 second. There will be either zero atoms left or one atom left, depending on whether or not the atom happens to decay.Instead, the half-life is defined in terms of probability. It is the time when the expected value of the number of entities that have decayed is equal to half the original number. For example, one can start with a single radioactive atom, wait its half-life, and measure whether or not it decays in that period of time. Perhaps it will and perhaps it will not. But if this experiment is repeated again and again, it will be seen that it decays within the half life 50% of the time.In some experiments (such as the synthesis of a superheavy element), there is in fact only one radioactive atom produced at a time, with its lifetime individually measured. In this case, statistical analysis is required to infer the half-life. In other cases, a very large number of identical radioactive atoms decay in the time-range measured. In this case, the central limit theorem ensures that the number of atoms that actually decay is essentially equal to the number of atoms that are expected to decay. In other words, with a large enough number of decaying atoms, the probabilistic aspects of the process can be ignored.There are various simple exercises that demonstrate probabilistic decay, for example involving flipping coins or running a computer program.

The radioactive half-life for a given radioisotope is the time for half the radioactive nuclei in any sample to undergo radioactive decay. After two half-lives, there will be one fourth the original sample, after three half-lives one eight the original sample, and so forth.

The radioactive half-life gives a pattern of reduction to half in any successive half-life period.

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Formulae for half-life in exponential decay A quantity is said to be subject to exponential decay if it decreases at a rate proportional to its value. Symbolically, this can be expressed as the following differential equation, where N is the quantity and λ is a positive number called the decay constant.

The solution to this equation is:

Here N(t) is the quantity at time t, and N0 = N(0) is the initial quantity, An exponential decay process can be described by any of the following three equivalent formulae:

Nt = N0e − t / τ

Nt = N0e − λt

where

N0 is the initial quantity of the thing that will decay (this quantity may be measured in grams, moles, number of atoms, etc.),

Nt is the quantity that still remains and has not yet decayed after a time t, t1 / 2 is the half-life of the decaying quantity, τ is a positive number called the mean lifetime of the decaying quantity, λ is a positive number called the decay constant of the decaying quantity.

The three parameters t1 / 2, τ, and λ are all directly related in the following way:

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where ln(2) is the natural logarithm of 2 (approximately 0.693).By plugging in and manipulating these relationships, we get all of the following equivalent descriptions of exponential decay, in terms of the half-life:

Regardless of how it's written, we can plug into the formula to get

Nt = N0 at t=0 (as expected—this is the definition of "initial quantity") Nt = (1 / 2)N0 at t = t1 / 2 (as expected—this is the definition of half-life) Nt approaches zero when t approaches infinity (as expected—the longer we wait,

the less remains).

Half-life in non-exponential decay Many quantities decay in a way not described by exponential decay—for example, the evaporation of water from a puddle, or (often) the chemical reaction of a molecule. In this case, the half-life is defined the same way as before: The time elapsed before half of the original quantity has decayed. However, unlike in an exponential decay, the half-life depends on the initial quantity, and changes over time as the quantity decays.As an example, the radioactive decay of carbon-14 is exponential with a half-life of 5730 years. If you have a quantity of carbon-14, half of it (on average) will have decayed after 5730 years, regardless of how big or small the original quantity was. If you wait another 5730 years, one-quarter of the original will remain. On the other hand, the time it will take a puddle to half-evaporate depends on how deep the puddle is. Perhaps a puddle of a certain size will evaporate down to half its original volume in one day. But if you wait a second day, there is no reason to expect that precisely one-quarter of the puddle will remain; in fact, it will probably be much less than that. This is an example where the half-life reduces as time goes on. (In other non-exponential decays, it can increase instead.)For specific, quantitative examples of half-lives in non-exponential decays, see the article Rate equation.A biological half-life is also a type of half-life associated with a non-exponential decay, namely the decay of the activity of a drug or other substance after it is introduced into the body.

Mean lifetime

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If the decaying quantity is the number of discrete elements of a set, it is possible to compute the average length of time for which an element remains in the set. This is called the mean lifetime (or simply the lifetime) and it can be shown that it relates to the decay rate,

The mean lifetime (also called the exponential time constant) is thus seen to be a simple "scaling time":

Thus, it is the time needed for the assembly to be reduced by a factor of e.A very similar equation has shown above, which arises when the base of the exponential is chosen to be 2, rather than e. In that case the scaling time is the "half-life".

Radioactive Equilibrium

Radioactive equilibrium for a decay chain occurs when the each radionuclide decays at the same rate it is produced. At equilibrium, all radio nuclides decay at the same rate. Understanding the equilibrium for a given decay series, helps scientists estimate the amount of radiation that will be present at various stages of the decay.

For example, as uranium-238 begins to decay to thorium-234, the amount of thorium and its activity increase. Eventually the rate of thorium decay equals its production--its concentration then remains constant. As thorium decays to proactinium-234, the concentration of proactinium-234 and its activity rise until its production and decay rates are equal. When the production and decay rates of each radionuclide in the decay chain are equal, the chain has reached radioactive equilibrium.

Equilibrium occurs in many cases. However if the half-life of the decay product is much longer than that of the original radionuclide, equilibrium cannot occur. The graphs below illustrate the progress of ingrowth, and its effect on overall activity, and the potential for radioactive equilibrium in three general cases.

For simplicity's sake, the illustrations assume that the decay chain is only two steps--the decay product decays to a stable nuclide. As decay chains lengthen, the calculations become more complex.

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We considered briefly a special case in which a radioactive daughter substance was formed in the decay of the parent. Let us take up the general case for the decay of a radioactive species, denoted by subscript 1, to produce another radioactive species, denoted by subscript 2. The behavior of N1 is just as has been derived; that is,

11 1

dNN

dt and

10 t

1 1N N e

where we use the symbol 01N to represent the value of N1 at t = 0.

Now the second species is formed at the rate at which the first decays, 1 1N , and itself

decays at the rate 2 2N . Thus

2

1 1 2 2

dNN N

dt

10 t21 1 2 2

dNN e N

dt

10 t22 2 1 1

dNN N e

dt

By multiplying both sides by 2te

:

2 12 2 tt t 022 2 1 1

dN te N e N e

dtwhat to be rewritten:

2 12 tt 0

2 1 1

dN e N e

dtIntegrating:

2 12 tt 01

2 12 1

N e N e C

1 20 t t1

2 12 1

N N e Ce

for t=0, N2 = 02N :

0 011 2

2 1

C N N

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1 2 20 t t 0 t12 1 2

2 1

N N e e N e(2)

The solution of 2

1 1 2 2

dNN N 0

dt this linear differential equation of the first order may be obtained by standard methods and gives

1 2 20 t t 0 t1

2 1 22 1

N N e e N e

where 02N is the value of N2 at t = 0. Notice that the first group of terms shows the

growth of daughter from the parent and the decay of these daughter atoms; the last term gives the contribution at any time from the daughter atoms present initially.In applying (2) to considerations of radioactive (parent and daughter) pairs, we can distinguish two general cases, depending on which of the two substances has the longer half life.

If the parent is longer-lived than the daughter (λ1<λ2), a state of so-called radioactive equilibrium is reached; that is, after a certain time the ratio of the numbers of atoms and, consequently, the ratio of the disintegration rates of parent and daughter become constant.

This can be readily seen from (2); after t becomes sufficiently large, 2te is negligible

compared with 1te , and

20 t2N e

also becomes negligible; then

10 t12 1

2 1

N N e

and, since 10 t

1 1N N e

1 1

2 2 1

NN

(3)

The relation of the two measured activities is found from 1 1 1 1A c N , 2 2 2 2A c N to be

1 2 11

2 2 2

cAA c

(4)In the special case of equal detection coefficients (c1=c2) the ratio of the two activities,

1 1

2 2

A1

A

,

may have any value between 0 and 1, depending on the ratio of λ1 to λ2 that is, in equilibrium the daughter activity will be greater than the parent activity by the factor λ2/( λ2 – λ1). In equilibrium both activities decay with the parent's half life.

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As a consequence of the condition of transient equilibrium (λ2>λ1), the sum of the parent and daughter disintegration rates in an initially pure parent fraction goes through a maximum before transient equilibrium is achieved. This situation is illustrated in figure 2.

Figure 2 - Transient equilibrium: (a) total activity of an initially pure parent fraction; (b)

activity due to parent ( 1/ 2t = 8.0 h); (c) decay of freshly isolated daughter fraction ( 1/ 2t

= 0.80 h); (d) daughter activity growing in freshly purified parent fraction; (e) total daughter activity in parent-plus-daughter fractions

38

The more general condition for the total measured activity (A1+A2) of an initially pure parent fraction to exhibit a maximum is found to be c2/c1 > λ1/λ2. This condition holds

regardless of the relative magnitudes of λ1, and λ2. The

2 1 2 1

2 1 2

cc

condition will give a maximum in the total measured activity that occurs at a negative time.

A limiting case of radioactive equilibrium in which 1 2 and in which the parent activity does not decrease measurably during many daughter half lives is known as secular equilibrium. Derive the equation as a useful approximation of (3):

1 1

2 2

NN

or 1 1 2 2N N

and the measured activities are equal if c1 =c2.

Figure 2 presents an example of transient equilibrium with 1 2 (actually with λ1/λ2 = 0.1); the curves represent variations with time of the parent activity and the activity of a freshly isolated daughter fraction, the growth of daughter activity in a freshly purified parent fraction, and other relations; in preparing the figure we have taken c1=c2. Figure 3 is a similar plot for secular equilibrium; it is apparent that as λ1, becomes smaller compared to λ2 the curves for transient equilibrium shift to approach more and more closely the limiting case shown in figure 3.

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Figure 3 - Secular equilibrium: (a) total activity of an initially pure parent fraction; (b)

activity due to parent ( 1/ 2t ); this is also the total daughter activity in parent-plus-

daughter fractions; (c) decay of freshly isolated daughter fraction ( 1/ 2 0.8t h ); (d) daughter activity growing in freshly purified parent fraction.

If the parent is shorter-lived than the daughter (λ1>λ2), it is evident that no equilibrium is attained at any time. If the parent is made initially free of the daughter, then as the parent decays the amount of daughter will rise, pass through a maximum, and eventually decay with the characteristic half life of the daughter. This is illustrated in figure 4; for this plot we have taken λ1/λ2= 10, and c1=c2. In the figure the final exponential decay of the daughter is extrapolated back to t=0.

Figure 4 - The case of no equilibrium: (a) total activity; (b) activity due to parent (

1/ 2 0.8t h ); (c) extrapolation of final decay curve to time zero; (d) daughter activity in initially pure parent.

This method of analysis is useful if 1 2 , for then this intercept measures the activity 0

2 2 1c N the 01N atoms give rise to N2 atoms so early that

01N may be set equal to the

extrapolated value of N2 at t = 0. The ratio of the initial activity 0

1 1 1c N to this extrapolated activity gives the ratios of the half lives if the relation between c1 and c2 is known:

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1021 1 1 1 1 2

02 2 1 2 2

12 1

tc N c

xc N c

t

If λ2 is not negligible compared to λ1, it can be shown that the ratio λ1/λ2 in this

equation should be replaced by

1 2

2

and the expression involving the half lives

changed accordingly.Both the transient-equilibrium and the no-equilibrium cases are sometimes analyzed in terms of the time tm for the daughter to reach its maximum activity when growing in a freshly separated parent fraction.This time we find from the general equation (2) by differentiating,

1 2

20 t 0 t2 1 1 21 1

2 1 2 1

dNN e N e

dt

and setting

2dN0

dt

when t = tm:

2 1 mt2

1

e

or

2m

2 1 1

1t ln

At this time the daughter decay rate 2 2N is just equal to the rate of formation 1 1N , [this is obvious from (1)]; in figures 2 and 4, in which we assumed c1=c2, we have the parent activity A1 intersecting the daughter growth curve d at the time tm. (The time tm is infinite for secular equilibrium.)

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Transient Equilibrium

When the half-life of the original radionuclide is only slightly longer or about the same as the half life of the decay product, the total activity rises initially. This results from the combined decay of both radio nuclides. (It peaks slightly before the activity of the decay product does.) Eventually a balance (equilibrium) is reached.

The total activity then decays at about the same rate as the original radionuclide. This is known as "transient equilibrium."

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Secular Equilibrium

When the half-life of the original radionuclide is much longer than the half-life of the decay product, the decay product generates radiation more quickly. Within about 7 half lives of the decay product, their activities are equal, and the amount of radiation (activity) is doubled. Beyond this point, the decay product decays at the same rate it is produced--a state called "secular equilibrium."

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No Equilibrium

If the half-life of the decay products is much longer than that of the original radionuclide, its activity builds up to a maximum and then declines. The original radionuclide eventually decays away and no equilibrium occurs.

Methodology First prepare a solution of Cs-Ba by using the mini generator. fill your syringe with eluting solution. Remove the stoppers on either end of the mini-generator column.

Hold the mini-generator carefully above the glass vial with the arrows on the mini-generator pointing downward. While your partner holds the glass vial, insert the syringe firmly into the hole on the top of the generator without pushing on the syringe plunger. While carefully holding the mini-generator and the vial, use the syringe to force about 10 drops (1 mL) of solution into the mini-generator. DO NOT SUCK UP ON THE SYRINGE; ONLY INSERT SOLUTION IN THE DIRECTION OF THE ARROWS ON THE MINI-GENERATOR. This will release the barium 137m into the glass vial. Once

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you’ve pushed the solution through, remove the syringe and place it and the mini-generator carefully back on the table.Place the sensor window of the Geiger counter directly next to the glass vial and you will hear an increase in the level of radiation, this is the radioactive decay of barium 137m into barium 137.Repeat this at least 15 times and record all of your data on your table for a total of at least 15 data points.Turn the Geiger counter off. Replace the stoppers on the two ends of the mini-generator and return any remaining eluting solution from your syringe into the bottle from which you removed it. Pour the contents of your glass vial into the HCl waste bottles, replace the cover on the glass vial and leave it with the “dirty vials.”

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Observations and Calculations

Sr. # Time(min) Activity(Cpm) ln(A)1 1 935 6.842 2 745 6.613 3 534 6.284 4 452 6.115 5 359 5.886 6 291 5.677 7 250 5.528 8 193 5.269 9 204 5.3110 10 160 5.0711 11 157 5.0512 12 130 4.8613 13 132 4.8814 14 109 4.6915 15 110 4.70

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Time to reach Equilibrium Point After five half lives the graph of decay and growth become parallel to each other So time, T after which equilibrium will established is

since half life of Ba = 2.6 so T = 13 min.

Now we will find which type of equilibrium has established.

From radioactive decay law

So

Where and

So ,

Thus

Now

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For Transient Equilibrium The condition for the Transient Equilibrium is

Now =

=

=

Now

and

So

For Transient Equilibrium the condition must be satisfied but from

above results and .

i.e. thus we can say that Transient Equilibrium is not established.

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For Secular Equilibrium The condition for the Secular Equilibrium is

So

And

Since Thus we can say that Secular Equilibrium has been established.

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Precautions and Sources of Errors Lab uses a sealed radioactive source. Within this mini-generator is radioactive cesium with a half-life of about 30 years. Because this source is sealed, you will not come into contact with this cesium unless the mini-generator is broken. Therefore, please be careful handling this piece of equipment. The radioactive barium that you will be working with today has a very short half-life. By the time the lab is over today, more than 10 half-lives will have passed, at which point the radioactivity levels are equal to the background radioactivity normally present in the air. Therefore, this radioactive source is very safe to work with AS LONG AS THE FOLLOWING SAFETY

No food or drinks are allowed in this lab; leave all food outside the lab room.

Smoking is never allowed in the lab.

Do not apply cosmetics during this lab session.

Safety goggles and gloves must be worn at all times when working with the radioisotope generators.

You must wear closed-toe shoes; no sandals may be worn.

The eluting solution contains a weak concentration of HCl, this can cause burns on your skin and clothing, please be careful to not spill it and wear gloves and goggles at all times.

Notify your lab instructor of any spills or accidents immediately.

Please do not touch the sensor window face plate on the Geiger counter; this can ruin this expensive piece of equipment.

Dispose of your used gloves in the trash and wash your hands thoroughly before leaving the lab.

Do not gather near the G.M counter otherwise it will not give you correct readings.

Quickly take the readings because it Ba-137m have a very short life.

Be careful with the radiations because Beta radiations are very dangerous.

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Questions and Answers

Question 1

Match the origination of the radionuclide with the most appropriate decay mode. (A) Bombarding with neutrons in a reactor(B) Bombarding with protons in a cyclotron(C) Mining pitchblende (i) Alpha emission(ii) Beta minus emission(iii) Beta plus emission

Answer:

A-ii  Adding neutrons to nuclei results in excess neutrons which leads to beta minus decay; B-iii;   Adding protons to nuclei requires them to lose their excess positive charge by positron emission or electron capture; C-i;    226Ra is an alpha emitter which decays to form radon (222Rn).

Question 2

True (T) or False (F). Radioactive equilibrium (A) is secular when the half-life of the parent » half-life of the daughter(B) requires about 6 half-lives for secular equilibrium to be established(C) is transient if the half-life of the parent is > half-life of the daughter(D) for a 99Mo/99mTc generator may be termed transient(E) is established in 24 hours for a 99Mo/99mTc generator.

Answer:

A-True; B-True; C-True; D-TrueE-True.

Question 3

 For 99mTc decaying to 99Tc, all of the following are true EXCEPT (A) the half-life of 99mTc is 67 hours(B) the half-life of 99Tc is 2.l x 105 years

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(C) activity is N x lambda (N = number of atoms; lambda is decay constant)(D) lambda= 0.693/T1/2 where T1/2 is the half-life

Answer:

A.    The half life of 99mTc is 6 hours. The parent of 99mTc, 99Mo has a half-life of 67 hours.

Question 4

If 100 mCi 99mTc is "milked" from a 99Mo generator (at equilibrium) at 9 A.M. on Monday, then (A) the activity of 99Mo is 50 mCi at 3 P.M. on Monday(B) 80 mCi 99mTc can be "milked" at 9 A.M. on Tuesday(C) 50 mCi 99mTc can be "milked" at 9 A.M. on Sunday(D) the generator can no longer be used for 99mTc production

Answer:

B.   It takes about 24 hours for transient equilibrium to be established between the 99Mo/99mTc. The activity of 99Mo will be 80 mCi since it decays with a half-life of 67 hours.

 Question 5.

The "ideal" radiopharmaceutical for imaging an organ in nuclear medicine studies would have (A) a short half-life(B) no particulate emissions(C) rapid clearance from the blood stream(D) photons with an energy of about 150 keV(E) all of the above Answer: E.    An ideal radiopharmaceutical would have all of these properties.

Question 6. The radiation level adjacent to the one week-old 99Mo/99mTc generator depends on all of the following EXCEPT the (A) initial activity of 99Mo(B) number of times the generator was milked

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(C) amount of Pb shielding around the generator(D) amount of 99Mo remaining(E) distance from the generator  Answer: B.    Elutions only affect the amount of 99mTc in the generator and since the 99mTc photon energy (140 keV) is very low, this will not contribute significantly to the measured radiation level outside the shielded generator.

Question 7.  Technetium-99m generators CANNOT be (A) produced in a cyclotron(B) used to dispense more than 1 Ci(C) shipped by air(D) purchased by licensed users(E) used for more than 67 hours  Answer: A. 99Mo may be produced in a reactor or from fission products, but cannot be produced in a cyclotron since 99Mo is a beta emitter requiring the addition of neutrons, not protons.

Question 8.  Match the following half-lives with the appropriate radionuclide. (A) 2 minutes(B) 110 minutes(C) 13 hours(D) 67 hours(E) 8 days (i) Fluorine-18(ii) Molybdenum-99(iii) Iodine-123(iv) Iodine-131(v) Oxygen-15  Answer:A-vB-iC-iiiD-iiE-iv

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Question 9.  Gamma camera crystals (A) are made of cesium iodide(B) convert 95% of gamma ray energy to light photons(C) are generally 100 μm thick for good resolution(D) have lead backing to minimize backscatter(E) have a high probability of absorbing 140 keV photons Answer: E. A typical Nal crystal thickness of 10 mm absorbs over 90% of the 140 keV photons via the photoelectric effect.

Question 10.   The pulse height analyzer in a gamma camera system (A) increases the detector efficiency(B) analyzes the total energy deposited in crystal(C) corrects the count rate losses due to "dead time"(D) performs a coincidence detection analysis(E) increases the count rate  Answer: B. The pulse height analyzer measures the total energy deposited in the photon interaction and "accepts" only photopeak interactions that correspond to a photoelectric interaction with the full photon energy.

Question 11.    Match the typical resolution at full width half maximum (FWHM) with the detection system. A.    Gamma camera (intrinsic) B.    Gamma camera (low-energy all-purpose collimatorC.    Gamma camera (high-resolution collimator) D.    PET  (i) 3mm(ii) 5mm(iii) 7.5 mm(iv) 10 mm Answer:A-i

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B-ivC-iiiD-ii

Question 12.     For each clinical application, match the best collimator. (A) Thyroid imaging(B) Pediatric study (C) Lung scan(D) Liver scan (i) Diverging(ii) Parallel hole(iii) Converging(iv) Pinhole Answer:A-iv; thyroid studies are normally performed using pinhole collimators to improve resolution; B-iii; converging collimator is used in pediatric studies to magnify the image; C-i; diverging collimators minify the image and permit both lungs to be visualized in a single image; D-ii; liver scans are normally performed with an all-purpose or high-resolution parallel hole collimator. Question 13.      For parallel hole collimators, which of the following improves as the distance from the face of the collimator is increased? (A) Resolution(B) Sensitivity(C) Energy resolution(D) Imaging time(E) None of the above  Answer: E. None of these factors improve. In clinical practice, it is important to minimize the patient collimator distance.

Question 14.       Nuclear medicine images acquired using a computer typically have (A) 500,000 to 1,000,000 counts(B) matrix sizes of 64 x 64 or 128 x 128

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(C) 256 gray scale levels(D) 4 to 16 kBytes of image data(E) all of the above Answer:  E. All of the statements are true.

Question 15.       In general, gamma camera system resolution with a parallel-hole collimator (A) is determined at full width half maximum (FWHM)(B) includes an intrinsic resolution of about 3 mm(C) depends on collimator sensitivity(D) deteriorates with distance from the collimator(E) all of the above  Answer: E. All of the statements are true.

Question 16.       The system resolution of a gamma camera with a parallel hole collimator improves with increased collimator (A) hole size(B) thickness(C) diameter(D) distance to patient(E) sensitivity  Answer: B. Increasing collimator thickness improves resolution but reduces sensitivity.

Question 17.       Thyroid imaging studies can be performed with all of the following EXCEPT (A) 99mTc pertechnetate(B) NaI uptake probe(C) 123 I(D) parallel hole collimator(E) pinhole collimator 

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Answer: B. An uptake probe measures the total amount of activity in the thyroid but does not generate any kind of image.

Question 18.        A circular cold spot artifact in a gamma camera image could NOT be the result of (A) a cracked NaI crystal(B) a metallic object on the patient(C) a defective photomultiplier tube(D) an incorrect photopeak energy setting of the PHA Answer: A.A cracked Nal crystal would give rise to a linear artifact, not a circular one.

Question 19.       Match the following half-life relationships. (A) Tb is very long(B) Tb is very short(C) Tb and T1/2 are equal(D) Tb and T1/2 are both very long (i) Negligible loss of activity(ii) Te = Tb(iii) Te = Tb/2(iv) Te = T1/2 Answer: A-ivB-ii; C-iii; D-i. All of these follow from the definition of effective half-life 1/Te = 1/T1/2 + 1/Tb.

Question 20.      When 99mTc is administered to a patient, which of the following CANNOT contribute to the patient dose? (A) Auger electrons(B) Beta particles(C) Internal conversion electrons(D) Gamma rays(E) Characteristic x-rays

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 Answer: B. There are no beta particles associated with 99mTc.

Question 21.       Which of the following statements regarding radioiodine and the fetal thyroid are true? (A) Inorganic iodine crosses the placenta(B) Iodine can concentrate in fetal thyroids(C) The highest risk is in the second and third trimesters(D) Fetal thyroid is not present before week 10 of pregnancy(E) All of the above Answer: E. All of the statements are true.

Question 22.      True (T) or False (F). For patients undergoing typical nuclear medicine procedures (A) effective dose equivalents are about 5 mSv (500 mrem) (B) the dose is lower than a chest x-ray examination(C) maximum organ doses are about 50 mGy (5 rad)(D) the effective dose equivalents are similar to PET studies(E) increasing the NM imaging time increases the dose Answer: A-True; B-False; typical HE for a PA chest x-ray is 20 microSv (2 mrem); C-True; D-True; although positron emitters are much shorter lived, they deposit much more energy per decay, and these two factors cancel each other out; E-False; patient dose is determined by the amount of activity administered, and "imaging" time is irrelevant to patient dose.

Question 23.      An ideal therapeutic radionuclide (e.g.32P) would have (A) high uptake in the organ of interest(B) high-energy beta decay(C) no high-energy gamma rays(D) a long biologic half-life in the organ of interest(E) all of the above

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Answer: E. All these characteristics are desirable in a therapeutic radionuclide because they maximize the organ dose and minimize external radiation hazards from gamma rays.

Question 24.      Match the following image characteristics with the appropriate equipment. (A)  Edge packing (B)  Linearity(C)  Uniformity(D) Distortion (i) Damaged collimator(ii) Flood source(iii) Line bar phantom(iv) Periphery of gamma camera  Answer: A-iv; edge packing is observed at the edge of nuclear medicine images; B-iii; line bar phantoms are used to ensure that the image is as straight as the object; Cii; gamma camera uniformity is assessed using flood sources; D-i; distortion may result from a damaged collimator.

Question 25.       Low-level radioactive wastes, such as tubing and swabs contaminated with 99mTc, may be monitored with (A) Geiger-Muller counters(B) film badge dosimeters(C) thermoluminescent dosimeters(D) ionization chambers(E) do not need to be monitored Answer: A.Geiger-Mtiller counters are generally used to monitor low-level waste because of their high sensitivity, portability, and immediate responses.

Question 26.       Match the radionuclide impurity with the corresponding radioactive material. (A)  123I capsules(B)  99mTc pertechnetate(C)  67Ga (D)  201Tl

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 (i) 99Mo(ii) 124I(iii) 202Tl(iv) None  Answer:A-ii; B-i; 99Mo may be eluted from the column; C-iv; 67Ga is produced in a cyclotron from 67Zn and has no radiochemical impurities; D-iii. Question 27.   True (T) or False (F). Single photon emission computed tomography (SPECT) normally requires (A)  positron emitting radioisotopes(B)  gamma camera rotation(C)  coincidence detection (D)  pulse height analysis(E) filtered back projection reconstruction algorithms(F) sampling of activity in patient's blood Answer:  A-False; positron emitters are required for PET imaging; B-True; projections are normally obtained through 360 degrees around the patient; C-False; annihilation radiation in PET is obtained using coincidence detection; D-True; this is required to minimize the amount of scatter accepted; E-True; filtered back projection algorithms are used in SPECT; F-False; this is occasionally done in PET to obtain absolute quantitative physiological data.

Question 28.   For SPECT, all the following are true - EXCEPT (A) 64 or 128 projections are obtained(B)  it takes about 20 minutes to perform(C)  corrections are usually made for patient motion(D) images show relative radioisotope concentrations(E) image quality is affected by scatter  Answer: C. Patient motion correction is not normally performed for SPECT imaging. Digital subtraction angiography imaging software sometime permits corrections to be made for patient motion.

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Question 29.  Advantages of PET over conventional gamma camera imaging include (A) a wider choice of molecules that may be labeled with positron emitters(B) better resolution(C) lower image noise(D) rapid decay of radiopharmaceutical(E) all of the above Answer:E. All of the statements are generally true in PET imaging. Question 30.  PET imaging systems (A) need high-energy parallel hole collimators(B) cannot handle very high count rates(C) suffer from significant attenuation losses(D) detect annihilation photons in coincidence

Answer:D Two 511 keV photons are emitted 180 degrees apart, which are detected by a coincidence circuit.

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To determine the absorption coefficient of lead for Gamma Rays using GM counter.

Aims The purpose of this experiment is to investigate various radiation phenomena using a Geiger-Mueller counter. The aim of this experiment is to illustrate

The effects of material thickness on the penetrating ability of gamma rays. How radiation flux changes with distance from the source. How intensity of a light changes with distance from the source. Affect of intervening absorbers on radiation from the source. To study the nature and source of gamma rays. To observe the modes of interaction of gamma rays with matter.

Objective To study the behavior of gamma rays and to determine the absorption coefficient in lead of the gamma radiation from the given source.

Equipment

G.M counter, Cesium Barium generator, solution of HCl, Stopwatch, Timer Scalar, led slides.

Theory Gamma Radiations Gamma rays (often denoted by the Greek letter gamma, γ) are an energetic form of electromagnetic radiation produced by radioactivity

or other nuclear or subatomic processes such as electron-position annihilation. Gamma rays are more penetrating than either alpha or beta radiation, but less ionizing. Gamma rays are distinguished from X rays by their origin. Gamma rays are produced by nuclear transitions while X-rays are produced by energy transitions due to accelerating electrons. Because it is possible for some electron transitions to be of higher energy than nuclear transition, there is an overlap between low energy gamma rays and high energy X-rays.

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Shielding for γ rays requires large amounts of mass. Shields that reduce gamma ray intensity by 50% include 1 cm (0.4 inches) of lead, 6 cm (2.4 inches) of concrete or 9 cm (3.6 inches) of packed dirt.

Gamma rays from nuclear fallout would probably cause the largest number of casualties in the event of the use of nuclear weapons in a nuclear war. An effective fallout shelter reduces human exposure at least 1000 times.

Gamma rays are less ionizing than either alpha or beta rays. However, reducing human danger requires thicker shielding. They produce damage similar to that caused by X-rays such as burns, cancer, and genetic mutations.

In terms of ionization, gamma radiation interacts with matter via three main processes: the photoelectric effect, Compton scattering, and pair production.

Photoelectric Effect: This describes the case in which a gamma photon interacts with and transfers all of its energy to an orbital electron, ejecting that electron from the atom. The kinetic energy of the resulting photoelectron is equal to the energy of the incident gamma photon minus the binding energy of the electron. The photoelectric effect is thought to be the dominant energy transfer mechanism for x-ray and gamma ray photons with energies below 50 keV (thousand electron volts), but it is much less important at higher energies.

Compton Scattering: This is an interaction in which an incident gamma photon loses enough energy to an orbital electron to cause its ejection, with the remainder of the original photon's energy being emitted as a new, lower energy gamma photon with an emission direction different from that of the incident gamma photon. The probability of Compton scatter decreases with increasing photon energy. Compton scattering is thought to be the principal absorption mechanism for gamma rays in the intermediate energy range 100 keV to 10 MeV (million electron volts), an energy spectrum which includes most gamma radiation present in a nuclear explosion. Compton scattering is relatively independent of the atomic number of the absorbing material.

Pair Production: By interaction in the vicinity of the coulomb force of the nucleus, the energy of the incident photon is spontaneously converted into the mass of an electron-positron pair. A positron is a positively charged electron. Energy in excess of the equivalent rest mass of the two particles (1.02 MeV) appears as the kinetic energy of the pair and the recoil nucleus. The electron of the pair, frequently referred to as the secondary electron, is densely ionizing. The positron has a very short lifetime. It combines within 10-8 second with a free electron. The entire mass of these two particles is then converted to two gamma photons of 0.51 MeV energy each.

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Gamma rays are often produced alongside other forms of radiation, such as alpha or beta. When a nucleus emits an α or β particle, the daughter nucleus is sometimes left in an excited state. It can then jump down to a lower level by emitting a gamma ray in much the same way that an atomic electron can jump to a lower level by emitting ultraviolet radiation.

Gamma rays, x-rays, visible light, and UV rays are all forms of electromagnetic radiation. The only difference is the frequency and hence the energy of the photons. Gamma rays are the most energetic. An example of gamma ray production follows.

First cobalt-60 decays to excited nickel-60 by beta decay:

Then the nickel-60 drops down to the ground state by emitting a gamma ray:

The probability of each of the three processes taking place in a given thickness of material depends on the energy of the photon and the atomic structure of the material. The total probability for interaction of photons in Pb, i.e., the sum of the probabilities of the three processes, varies with photon energy as indicated in Figure . The ordinate plotted on the graph is μ, the total linear absorption coefficient in units of . It is defined by the equation:

where N is the number of incident photons and dN is the number removed from the beam (i.e. absorbed) in an absorber of thickness dx (in cm). Note that dN and dx are the calculus equivalents of infinitesimally small values of ΔN and Δx, respectively. As in any process where the rate of decrease is proportional to the number present (such as the discharge of a capacitor), the solution of this differential equation is:

where N(x) is the number of photons passing through x cm of absorber and at x = 0 and e is the base of natural logarithms.

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The K absorption edge of lead is at 88keV yet it emits X-rays at only 75keV.

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Gamma-ray astronomy Gamma-ray astronomy is the astronomical study of gamma rays. Long before experiments could detect gamma rays emitted by cosmic sources, scientists had known that the universe should be producing these photons. Work by Feenberg and Primakoff in 1948, Hayakawa and Hutchinson in 1952, and, especially, Morrison in 1958 had led scientists to believe that a number of different processes which were occurring in the universe would result in gamma-ray emission. These processes included cosmic ray interactions with interstellar gas, supernova explosions, and interactions of energetic electrons with magnetic fields. However, it was not until the 1960s that our ability to actually detect these emissions came to pass.

Gamma-rays coming from space are mostly absorbed by the Earth's atmosphere. So gamma-ray astronomy could not develop until it was possible to get our detectors above all or most of the atmosphere, using balloons or spacecraft. The first gamma-ray telescope carried into orbit, on the Explorer-XI satellite in 1961, picked up fewer than 100 cosmic gamma-ray photons. These appeared to come from all directions in the Universe, implying some sort of uniform "gamma-ray background". Such a background would be expected from the interaction of cosmic rays (very energetic charged particles in space) with gas found between the stars.

Significant gamma-ray emission from our galaxy was first detected in 1967 by the gamma-ray detector aboard the OSO-3 satellite. It detected 621 events attributable to cosmic gamma-rays. However, the field of gamma-ray astronomy took great leaps forward with the SAS-2 (1972) and the COS-B (1975-1982) satellites. These two satellites provided an exciting view into the high-energy universe (sometimes called the 'violent' universe, because the kinds of events in space that produce gamma-rays tend to be explosions, high-speed collisions, and such). They confirmed the earlier findings of the gamma-ray background, produced the first detailed map of the sky at gamma-ray wavelengths, and detected a number of point sources. However, the poor resolution of the instruments made it impossible to identify most of these point sources with individual stars or stellar systems.

Perhaps the most spectacular discovery in gamma-ray astronomy came in the late 1960s and early 1970s from a constellation of defense satellites which were put into orbit for a completely different reason. Detectors on board the Vela satellite series, designed to detect flashes of gamma-rays from nuclear bomb blasts, began to record bursts of gamma-rays -- not from the vicinity of the Earth, but from deep space! Today, these gamma-ray bursts are seen to last for fractions of a second to minutes, popping off like cosmic flashbulbs from unexpected directions, flickering, and then fading after briefly dominating the gamma-ray sky. Studied for over 25 years now with instruments on board a variety of satellites and space probes, including Soviet Venera spacecraft and the Pioneer Venus Orbiter, the sources of these enigmatic high-energy flashes remain a mystery. They appear to come from far away in the Universe, and currently the most likely theory seems to be that at least some of them come from so-called hyper nova explosions - supernovas creating black holes rather than neutron stars.

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In 1977, NASA announced plans to build a "great observatory" for gamma-ray astronomy. The Compton Gamma-Ray Observatory (CGRO) was designed to take advantage of the major advances in detector technology during the 1980s, and was launched in 1991. The satellite carried four major instruments which have greatly improved the spatial and temporal resolution of gamma-ray observations. The CGRO provided large amounts of data which are being used to improve our understanding of the high-energy processes in our Universe. CGRO was de-orbited in June 2000 as a result of the failure of one of its stabilizing gyroscopes.

Currently, the main gamma ray observatory is the International Gamma-Ray Astrophysics Laboratory, (INTEGRAL). INTEGRAL is an ESA mission with contributions from Czech, Poland, USA and Russia. It was launched on 17 October 2002.

Gamma-ray astronomy is still mostly dominated by the quality of data. More and better data from newer missions and better instruments is therefore essential for progress in the field.

Gamma ray burster

In astronomy, Gamma-ray bursters (GRBs) are flashes of gamma rays that last from seconds to hours, the longer ones being followed by several days of X-ray after glow. They occur at random positions in the sky several times each day. As of summer 2003, one of the more promising but still highly speculative ideas is that with the creation of a black hole from a dying star. The black hole, surrounded by a rotating disk of matter falling into it somehow emits energetic beam parallel to the axis of rotation. However, the astrophysical community is still some distance away from coming to a consensus on the mechanism for GRB's, although most are optimistic that the puzzle will be solved by 2010.

The Discovery of GRB’s

Cosmic gamma-ray bursts were discovered in the late 1960s by the US "Vela" nuclear test detection satellites. The Velas were launched to detect radiation emitted by weapons tests, but they picked up occasional bursts of gamma rays from unknown sources. While the sensors on the Vela satellites had low angular resolution, in 1973 researchers at the US Los Alamos National Laboratory in New Mexico were able to use the data from the satellites to determine that the bursts came from deep space.

Gamma ray bursts can only be observed directly from space, as the atmosphere blocks gamma rays. Astronomers believed that once better gamma-ray detectors were put in orbit, they would be able to quickly pin down the locations of the GRB’s. After all, that is what happened with X-ray sources. However, when such improved detectors were sent into space in the 1970s, optical searches of the regions where the bursts originated showed nothing of interest. The sensors were not accurate enough to pinpoint the location of the bursts for detailed study.

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Further information on the burst sources proved hard to obtain, and led to more questions than answers. The first question posed by the GRB’s was: are they local to our own Galaxy, or do they occur in the distant reaches of the Universe? The second question was: what mechanism causes the bursts? If they do occur in the distant Universe, the mechanism must be producing enormous amounts of energy.

Little progress was made on the matter through the 1980s, but in April 1991, the US National Aeronautics and Space Administration (NASA) launched the "Compton Gamma Ray Observatory" on board the space shuttle. One of the instruments on board Compton was the "Burst & Transient Source Experiment (BATSE)", which could detect gamma-ray bursts and locate their positions in the sky with reasonable accuracy. BATSE established that there were at least two categories of gamma ray bursters: hard gamma ray bursters and soft gamma ray repeaters.

Within a year, BATSE determined that GRB’s occur twice or three times a day, and are randomly distributed over the entire sky. If they were events occurring in our own Galaxy, they would be preferentially distributed in the plane of the Milky Way. Even if they were associated with the galactic halo, they would still be preferentially distributed towards the galactic center, 30,000 light years away, unless the halo were truly enormous. Besides, if that were the case, nearby galaxies would be expected to have similar haloes, but they did not show up as "hot spots" of faint gamma-ray bursts.

To many astronomers, this implied that the GRB’s originated in the distant Universe, but that led to the problem of finding a mechanism that could generate so much energy. Other theorists were also still able to come up with "local" models for the GRB’s, and BATSE couldn't resolve the issue.

Uses

The powerful nature of gamma-rays has made them useful in the sterilizing of medical equipment by killing bacteria. They are also used to kill bacteria in foodstuffs to keep them fresher for longer. In spite of their cancer-causing properties, gamma rays are also used to treat some types of cancer. Multiple concentrated beams of gamma rays are directed on the growth in order to kill the cancerous cells. The beams are aimed from different angles to focus the radiation on the growth while minimizing damage to the surrounding tissues.

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Use Full Gammas

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Methodology

First prepare a solution of Cs-Ba by using the mini generator. fill your syringe with eluting solution. Remove the stoppers on either end of the mini-generator column.

Hold the mini-generator carefully above the glass vial with the arrows on the mini-generator pointing downward. While your partner holds the glass vial, insert the syringe firmly into the hole on the top of the generator without pushing on the syringe plunger. While carefully holding the mini-generator and the vial, use the syringe to force about 10 drops (1 mL) of solution into the mini-generator. DO NOT SUCK UP ON THE SYRINGE; ONLY INSERT SOLUTION IN THE DIRECTION OF THE ARROWS ON THE MINI-GENERATOR. This will release the barium 137m into the glass vial. Once you’ve pushed the solution through, remove the syringe and place it and the mini-generator carefully back on the table.Place the sensor window of the Geiger counter directly next to the glass vial and you will hear an increase in the level of radiation, this is the radioactive decay of barium 137m into barium 137.Place the source container directly under the G-M counter. The distance source (collimator) outlet-counter should be about 10cm.Remove the container lid.

Set the HV supply switch at zero volts. Branch all the segments of the set-upon .StartThe scalar. Slowly increase the high voltage (do not over come 1400V!), until youObserve the scalar to start counting the pulses. Lower the high voltage and find theStarting point (corresponding voltage) once again.

Perform about 10 measurements of the radiation intensity, beginning with the startingVoltage and increasing each time the operating voltage for 20V. The measurement timeShould be of the order of 30 seconds. If the registered intensity increases sharply for aSubsequent measurement do not continue.

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Set the operating voltage about 100V above the starting point. Carry out the measurement of the back ground, i.e. the intensity of radiation with the source well shut andPlaced at 1meter distance from the counter (at least).This measurement should be doneWith the measuring time of the order of 500 seconds.

Bring the source back and place it under the counter. Open the lid. Carry out theAbsorption measurements for at least two sets of plates out of three available (Pb, Al, andCu).The measurements should be carried out with the measuring time selected in suchA manner that the total count is not lower than 1000.Start with measurement with outAny absorbing plate and carry on placing on the source container subsequent plates. TheThickness of each plate should be measured with the help of micrometric screw. TheResults should be gathered in the table.Repeat this at least 15 times and record all of your data on your table for a total of at least 15 data points.Turn the Geiger counter off. Replace the stoppers on the two ends of the mini-generator and return any remaining eluting solution from your syringe into the bottle from which you removed it. Pour the contents of your glass vial into the HCl waste bottles, replace the cover on the glass vial and leave it with the “dirty vials.”

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Observations and Calculations

No. of slides Density (g/cm2) Time(min) Activity (Cpm)1 1.8 1 812 2.4 2 513 2.7 3 414 3.8 4 525 5.7 5 586 7.9 6 547 710.5 7 548 14.2 8 33

We know that linear absorption coefficient is µ = .693/HVT Where HVT is the half value thickness and is HVT = x-x/2 In this equation x is the time of any activity and x/2 is its half. Now when activity is81 then x = 1min and when activity becomes then x/2 = 3min, and HVT = 1-3 = -2minThus linear absorption coefficient is, µ = .693/2 = .347We also know that the mass absorption coefficient is µm = µ/ total densityFrom the table total density = 49g/cm2

Thus µm = .347/49 = .007Now max energy Max E = µ (measured)/µ (standard)We know that, µ (standard) = .7068Thus, Max E = .347/.7068 = 0.4905 = 0.5MevSince Max E for Cs, Ba-137 in case of gamma decay is .66MevThus % error = (0.66-0.5)x100/0.66 =24.2%

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Precautions and Sources of Errors Lab uses a sealed radioactive source. Within this mini-generator is radioactive cesium with a half-life of about 30 years. Because this source is sealed, you will not come into contact with this cesium unless the mini-generator is broken. Therefore, please be careful handling this piece of equipment. The radioactive barium that you will be working with today has a very short half-life. By the time the lab is over today, more than 10 half-lives will have passed, at which point the radioactivity levels are equal to the background radioactivity normally present in the air. Therefore, this radioactive source is very safe to work with AS LONG AS THE FOLLOWING SAFETY

No food or drinks are allowed in this lab; leave all food outside the lab room.

Smoking is never allowed in the lab.

Do not apply cosmetics during this lab session.

Safety goggles and gloves must be worn at all times when working with the radioisotope generators.

You must wear closed-toe shoes; no sandals may be worn.

The eluting solution contains a weak concentration of HCl, this can cause burns on your skin and clothing, please be careful to not spill it and wear gloves and goggles at all times.

Notify your lab instructor of any spills or accidents immediately.

Please do not touch the sensor window face plate on the Geiger counter; this can ruin this expensive piece of equipment.

Dispose of your used gloves in the trash and wash your hands thoroughly before leaving the lab.

Do not gather near the G.M counter otherwise it will not give you correct readings.

Quickly take the readings because it Ba-137m have a very short life.

Be careful with the radiations because Gamma radiations are very dangerous.

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Questions and Answers

What are Gamma Rays?

Gamma-rays have the smallest wavelengths and the most energy of any other wave in the electromagnetic spectrum. These waves are generated by radioactive atoms and in nuclear explosions. Gamma-rays can kill living cells, a fact which medicine uses to its advantage, using gamma-rays to kill cancerous cells.

Gamma-rays travel to us across vast distances of the universe, only to be absorbed by the Earth's atmosphere. Different wavelengths of light penetrate the Earth's atmosphere to different depths. Instruments aboard high-altitude balloons and satellites like the Compton Observatory provide our only view of the gamma-ray sky.

Gamma-rays are the most energetic form of light and are produced by the hottest regions of the universe. They are also produced by such violent events as supernova explosions or the destruction of atoms, and by less dramatic events, such as the decay of radioactive material in space. Things like supernova explosions (the way massive stars die), neutron stars and pulsars, and black holes are all sources of celestial gamma-rays.

How do we "see" using gamma-ray light?

Gamma-ray astronomy did not develop until it was possible to get our detectors above all or most of the atmosphere, using balloons or spacecraft. The first gamma-ray telescope,

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carried into orbit on the Explorer XI satellite in 1961, picked up fewer than 100 cosmic gamma-ray photons!

Unlike optical light and X-rays, gamma rays cannot be captured and reflected in mirrors. The high-energy photons would pass right through such a device. Gamma-ray telescopes use a process called Compton scattering, where a gamma-ray strikes an electron and loses energy, similar to a cue ball striking an eight ball.

This image shows the CGRO satellite being deployed from the Space Shuttle orbiter. This picture was taken from an orbiter window. The two round protrusions are one of CGRO's instruments, called "EGRET".

Who discovered gamma radiation?

Physicists credit French physicist Henri Becquerel with discovering gamma radiation. In 1896, he discovered that uranium minerals could expose a photographic plate through a heavy opaque paper. Roentgen had recently discovered x-rays, and Becquerel reasoned that uranium emitted some invisible light similar to x-rays. He called it "metallic phosphorescence."

In reality, Becquerel had found gamma radiation being emitted by radium-226. Radium-226 is part of the uranium decay chain and commonly occurs with uranium.

What are the properties of gamma radiation?

Gamma radiation is very high-energy ionizing radiation. Gamma photons have about 10,000 times as much energy as the photons in the visible range of the electromagnetic spectrum.

Gamma photons have no mass and no electrical charge--they are pure electromagnetic energy.

Because of their high energy, gamma photons travel at the speed of light and can cover hundreds to thousands of meters in air before spending their energy. They can pass through many kinds of materials, including human tissue. Very dense materials, such as lead, are commonly used as shielding to slow or stop gamma photons.

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Their wave lengths are so short that they must be measured in nanometers, billionths of a meter. They range from 3/100ths to 3/1,000ths of a nanometer.

What is the difference between gamma rays and x-rays?

Gamma rays and x-rays, like visible, infrared, and ultraviolet light, are part of the electromagnetic spectrum. While gamma rays and x-rays pose the same kind of hazard, they differ in their origin. Gamma rays originate in the nucleus. X-rays originate in the electron fields surrounding the nucleus or are machine-produced.

What conditions lead to gamma ray emission?

Gamma radiation emission occurs when the nucleus of a radioactive atom has too much energy. It often follows the emission of a beta particle.

What happens during gamma ray emission?

Cesium-137 provides an example of radioactive decay by gamma radiation. When a neutron transforms to a proton and a beta particle. The additional proton changes the atom to barium-137. The nucleus ejects the beta particle. However, the nucleus still has too much energy and ejects a gamma photon (gamma radiation) to become more stable.

How do we use gamma emitters?

Gamma emitting radio nuclides are the most widely used radiation sources. The penetrating power of gamma photons has many applications. However, while gamma rays penetrate many materials, they do not make them radioactive. The three radio nuclides by far most useful are cobalt-60, cesium-137, and technetium-99m.

Uses of Cesium-137: cancer treatment measure and control the flow of liquids in numerous industrial processes investigate subterranean strata in oil wells measure soil density at construction sites ensure the proper fill level for packages of food, drugs and other products.

Uses of Cobalt-60: sterilize medical equipment in hospitals pasteurize certain foods and spices treat cancer gauge the thickness of metal in steel mills.

Uses of Technetium-99m:

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TC-99m is the most widely used radioactive isotope for diagnostic studies. (Technetium-99m is a shorter half-life precursor of technetium-99.) Different chemical forms are used for brain, bone, liver, spleen and kidney imaging and also for blood flow studies.

In manufacturing, gamma radiation from cobalt-60 or cesium-137 can improve the physical characteristics of materials. For example, exposure to gamma radiation improves the durability of some wood and plastic composites. Treated materials can be used for flooring in high-traffic areas of department stores, airports, and hotels, because they resist abrasion and ensure low maintenance.

Another process, industrial radiography, uses gamma radiation to inspect metal parts and welds for defects. A sealed radiation source, usually iridium-192 or cobalt-60, beams gamma radiation at the part. Any gamma radiation passing through a crack or incomplete weld exposes special photographic, or radiographic, film. (The process is similar to taking an x-ray of a broken arm.) For example, manufacturers use radiography to inspect jet engine turbine blades.

How does gamma radiation change in the environment?

Gamma rays travel at the speed of light and exist only as long as they have energy. Once their energy is spent, whether in air or in solid materials, they cease to exist. The same is true for x-rays.

How are people exposed to gamma radiation?

Most people's primary source of gamma exposure is naturally occurring radionuclides, particularly potassium-40, which is found in soil and water, as well as meats and high-potassium foods such as bananas. Radium is also a source of gamma exposure. However, the increasing use of nuclear medicine (e.g., bone, thyroid, and lung scans) contributes an increasing proportion of the total for many people. Also, some man-made radionuclides that have been released to the environment emit gamma rays.

Most exposure to gamma and x-rays is direct external exposure. Gamma and x-rays can easily travel great distances through air and penetrate several centimeters in tissue. Most have enough energy to pass through the body, exposing all organs. X-ray exposure of the public is almost always in the controlled environment of dental and medical procedures.

Although they are generally classified as an external hazard; gamma emitting radio nuclides can also be inhaled, or ingested with water or food, and cause exposures to organs inside the body. Depending on the radionuclide, they may be retained in tissue, or cleared via the urine or feces.

Does the way a person is exposed to gamma or x-rays matter?

Both direct (external) and internal exposure to gamma rays or X-rays are of concern. Gamma rays can travel much farther than alpha or beta particles and have enough energy

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to pass entirely through the body, potentially exposing all organs. A large portion of gamma radiation largely passes through the body without interacting with tissue--the body is mostly empty space at the atomic level and gamma rays are vanishingly small in size. X-rays behave in a similar way, but have slightly lower energy. By contrast, alpha and beta particles inside the body lose all their energy by colliding with tissue and causing damage.

Gamma rays can ionize atoms in tissue directly or cause what are known as "secondary ionizations." Ionizations are caused when energy is transferred from gamma rays to atomic particles such as electrons (which are essentially the same as beta particles). These energized particles then interact with tissue to form ions through secondary ionizations. Because gamma rays are photons and thus interact less frequently with matter than alpha and beta particles, they are more penetrating and the damage they cause can occur much farther into tissue (that is, farther from the source of radiation).

How can gamma radiation affect people's health?

Because of the gamma ray's penetrating power and ability to travel great distances, it is considered the primary hazard to the general population during most radiological emergencies. In fact, when the term "radiation sickness" is used to describe the effects of large exposures in short time periods, the most severe damage almost certainly results from gamma radiation.

How do I know I'm near gamma emitters and gamma radiation?

You need specialized equipment to detect gamma radiation. You cannot see, or feel radiation hitting your body. However, you should be familiar with radiation warning symbols. You can protect yourself by avoiding devices with this symbol, and not entering areas where the symbol is posted.

How do I protect myself from x-ray and gamma radiation?

Your exposure to x-rays is almost entirely from dental and medical x-rays, including mammograms. The best way to protect yourself from excessive radiation from x-rays is to make sure the technician performing the procedure has the proper qualifications, and to simply ask questions. You might inquire about the necessity of having an x-ray, or receive assurance the x-ray machine has been inspected recently and that it is properly calibrated. You should be aware of steps taken to prevent exposures to other parts of your body (for example, through the use of a lead apron).

It is possible that you or a member of your family may encounter an industrial instrument or device containing a gamma radiation source. Every year, hundreds of devices containing radiation sources are lost, stolen, or otherwise enter the general public by mistake. For example:

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A factory that has gone out of business may contain one or more such devices. As the building structure is being dismantled, these forgotten devices often are considered as scrap metal, or someone may think they have value and try to sell them.

These devices should be avoided. You may recognize them by the radiation symbol, which means the device is radioactive. You should also look for identifying information such as "Nuclear Regulatory Commission" or the name of a radionuclide. Sometimes the radioactive markings may be covered over and not visible.

If you find a device you think may be radioactive, stay away from it, and promptly call your state radiation control program.

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Verification of Inverse Square Law.

Aims The aim of this experiment is to study the dependence of intensity of radiation on the distance from its source.

Objective The objective of this experiment is to verify Inverse Squarer Law.

Equipment

G.M counter, Cesium Barium generator, solution of HCl, Stopwatch, Timer Scalar.

Over View In the previous investigation we looked at the statistical interpretation of radioactive decay. When the decay particles are emitted they have equal probability of decaying in any direction. If we have a detector of constant area, we will detect more particles the closer we are to the source. As we move further away, we will count fewer, because we are subtending a smaller solid angle of the source. We believe there should, therefore, be

a dependence of the count rate as we move further away from the source with a

detector of constant area.

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Methodology

To verify the dependence of the radiation intensity, you vary the distance between

the source and detector by moving the lens holder (holding the source) along the optical bench. You will not need any additional material for this investigation.

1. The radioactive source should still be mounted on the lens holder. Vary the distance r between source and counter in 5 cm steps from 5 to 40 cm and measure the counting rate As a function of distance. If you are not able to get as close as 5 cm, do the best you can. The distance should be measured to the entrance window of the GM tube, which is Recessed inside the cylindrical tube. PLEASE REMEMBER TO NEVER TOUCH THIS ENTRANCE Slide the rubber o-ring that is around the WINDOW! Outside of the GM tube cylinder to the approximate position of the entrance window. You will just have to Approximate this, the best you can. Then make your measurements to the middle of the o-ring.

2. Choose a time interval (try 100 s) such that your number of counts is about 10000 at the 5 cm separation. Use this time interval for the rest of this part of the experiment. 3. Put your data results in Table 2-1 and in the appropriate column of the Excel file L13.A2-1. DistanceDependence.xls4. Now remove the Cs far away from the GM tube and take a background measurement for 250 s.

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Observations and Calculations

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Conclusion

The intensity (illuminance or irradiance ) of light or other linear waves radiating from a point source  (energy per unit of area perpendicular to the source) is inversely proportional to the square of the distance from the source; so an object (of the same size) twice as far away, receives only ¼ the energy (in the same time period).More generally, the irradiance , i.e., the intensity (or power per unit area in the direction of propagation ), of a spherical wave front varies inversely with the square of the distance from the source (assuming there are no losses caused by absorption or scattering).For example, the intensity of radiation from the sun is 9140 watts per square meter at the distance of Mercury (0.387AU); but only 1370 watts per square meter at the distance of earth (1AU)—a threefold increase in distance results in a ninefold decrease in intensity of radiation.Photographers and theatrical lighting professionals use the inverse-square law to determine optimal location of the light source for proper illumination of the subject.

The fractional reduction in electromagnetic fluence (F) for indirectly ionizing radiation with increasing distance from a point source can be calculated using the inverse-square law. Since emissions from a point source have radial directions, they intercept at a perpendicular incidence. The area of such a shell is 4pr2 where r is the radial distance from the center.The law is particularly important in diagnostic radiography and radiotherapy treatment planning, though this proportionality does not hold in practical situations unless source dimensions are much smaller than the distance r. Examples Let the total power radiated from a point source, e.g., an omni directional isotropic antenna , be . At large distances from the source (compared to the size of the source), this power is distributed over larger and larger spherical surfaces as the distance from the source increases. Since the surface area of a sphere of radius is , then intensity  of radiation at distance is the energy or intensity decreases by a factor of ¼ as the distance is doubled, or measured in dB it would decrease by 6.02 dB. This is the fundamental reason why intensity of radiation , whether it is electromagnetic or acoustic radiation, follows

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the inverse-square behaviour, at least in the ideal 3 dimensional context (propagation in 2 dimensions would follow a just an inverse-proportional distance behaviour and propagation in one dimension, the plane wave , remains constant in amplitude even as distance from the source changes).Questions and Answers What is the general equation of inverse square law?Some physical effect is reduced in proportion to the square of the distance from it's source. It applies to most forces or energies that radiate from a single point, like a light bulb. If you move twice as far from the light source, you will receive only a quarter as much light. And if you move three times as far from the bulb, you will receive only 1/9 as much. 1/4 is the inverse of 22 and 1/9 is the inverse of 32.

If you are using the acoustics it is different, because the sound pressure is inversely proportional to the distance (1/r) from the source. That is the inverse distance law.

Why is the intensity of gamma radiation proportional to an inverse square relationship of distance?

It is because the radiation spreads out over a surface area as it moves away from the source, and that surface area increases as R^2.

What is Nuclear Medicine?

Nuclear Medicine is the medical specialty that uses very small amounts of radioactive material to diagnose and treat disease. These materials, or tracers, are substances that are attracted to specific organs or tissues by the nature of their chemical makeup. The tracer emit energy, in the form of radiation, that is detectable by highly specialized equipment known as gamma cameras or scintillation cameras. The information (in the form of energy) is collected by the camera system and is transformed into images, which provide anatomical and functional detail of the body part being imaged.

What are the radiation hazards associated with the Nuclear Medicine patient?

Nuclear Medicine procedures are very safe. A patient only receives an extremely small amount of tracer, just enough to provide sufficient diagnostic information. The patient dose, in many cases, is equal to or less than common X-ray procedures. Most tracers pass quickly from the body through normal bodily functions. Patients should be encouraged to drink additional fluids as this will aid in eliminating the tracer more quickly.

Are there special precautions for pregnant staff when handling patients who have had a Nuclear Medicine procedure?

For most diagnostic procedures there would be no need for pregnant staff to take any additional precautions other than limiting their direct contact to as short as necessary. Radiation exposure follows the inverse square law which makes it dependant on both

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time and distance from the source. The inverse square law states that if you double your distance from the source your exposure rate drops by a factor of four, or if you triple your distance, your exposure drops by a factor of nine. This, combined with the fact that most diagnostic procedures use very small doses, means that the risk to hospital staff is very small. Any patients receiving a therapeutic Nuclear Medicine procedure should be handled by you after consultation with the Radiation Safety Officer and in accordance with the policies of the respective institutions.

Are Nuclear Medicine procedures performed on children?

Yes, Nuclear Medicine procedures are commonly performed on children and are generally used to evaluate bone pain, injuries, kidney or bladder conditions or infections. The dose for the patient is adjusted according to the child's age and weight. Sedation is sometimes required depending on the test being performed and the child.

Why are there delays between Nuclear Medicine procedures and not between X-ray or Ultrasound procedures?

Nuclear Medicine procedures often use the same radioactive tracer combined with different chemical elements to visualize different organ or tissue systems. As these products break down and are eliminated from the body they would interfere with the imaging of another organ system as they would no longer be found only in the target organ or tissue. The Nuclear Medicine camera systems would not be able to differentiate the target organ or system from that of a previous test. For the most common tracer of Technetium it generally takes up to 48 hours to clear the body before another test can be ordered. Isotopes such as Gallium and Iodine can take considerably longer.

What amount of radiation exposure is safe to receive?

There is no dose below which radiation induced injury is absent. Every X-ray exposure involves risk. The benefits of radiation exposure should outweigh the risks, therefore, occupational exposure should be at its absolute minimum.

What kind of protective devices are available to me if I must be near an area where X-ray exposures are taken?

A lead apron is worn that covers 80% of your bone marrow. A thyroid shield is often used to protect the thyroid gland. Lead gloves protect your hands if you are supporting or assisting a patient who is having an X-ray and your hands are in close proximity to the X-ray beam. However, radiation effects to the skin and extremities are non-existent at today's dose levels.

How many portable chest X-rays can be taken in our area in one month?

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The intensity of radiation one (1) metre from the portable is so small that a radiation worker would have to be exposed to 2000 films a month to reach the dosage allowed the general public.

Where is the best place to stand during an X-ray if you are assisting?

If you are holding or supporting a patient always stand off to the side so that the X-ray beam is not pointing at you. No one should routinely hold or assist a patient during an X-ray exam.

Why are the patient's gonads protected during a chest or foot X-ray?

This is a radiation safety precaution to protect the patient from scattered radiation. The impact of radiation exposure on future generations has always been a concern. Radiation can produce mutations through unrepaired structural breaks in chromosomes or through changes in the order based on the DNA chain. If this occurs in germ cells it can be transmitted to future generations. Female patients between the ages of 11 - 55 years are questioned as to the possibility of pregnancy before irradiation. All patients are given gonadal shielding routinely up until the age of 55 years.

What are the primary risks to the general public from medical radiation?

The primary risks are called stochastic effects. These effects include carcinogenic and genetic effects. Ordering physicians consider the risks associated with an X-ray procedure vs the benefits of a speedy diagnosis and treatment for the patient.

How can I help to minimize medical X-ray exposure to my patients?

The largest source of unnecessary patient dose is unnecessary X-ray examinations. You can minimize exposure through communication. For example: questioning the orders for routine examinations. These should never be performed when there is no precise medical indication. Routine chest X-rays for hospital admission or annual physicals or asymptomatic patients are not necessary. Check to see if the patient has had X-rays done through the emergency department before being admitted to your floor. Ask the patient if recent films of the area of interest were performed at another site or clinic or under another physician.

What factors should I consider to reduce my occupational exposure?

Occupational exposure can be reduced by the effective use of time, distance and appropriate shielding. Take the following steps:

- reduce the amount of time spent in the area of the radiation source- remain as far from the source as possible. The inverse square law states that if you

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double your distance from the source your exposure rate drops by a factor of four, or if you triple your distance your exposure drops by a factor of nine.- utilize the use of fixed barriers or mobile shields as well as lead aprons and thyroid collars.

To study Random Processes and fluctuations in Random processes (Gaussian distribution Curve).

Aims The aim of this experiment is to make students familiar with the Gaussian Distribution Curve method i.e. how to handle the randomness.

Objective The objective of this experiment is to understand the random nature of radioactivity.

Equipment G.M Counter, Timer Scalar, Stop Watch, Radioactive Source.

Theory G.M Tube

A Geiger-Mueller (GM) tube is a gas-filled radiation detector. It commonly takes the form of a cylindrical outer shell (cathode) and the sealed gas-filled space with a thin central wire (the anode) held at ~ 1 KV positive voltage with respect to the cathode. The fill gas is generally argon at a pressure of less than 0.l atm plus a small quantity of a quenching vapor (whose function is described below).

If a gamma - ray interacts with the GM tube (primarily with the wall by either the Photoelectric Effect or Compton scattering) it will produce an energetic electron that may pass through the interior of the tube.

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Ionization along the path of the primary electron results in low energy electrons that will be accelerated towards the center wire by the strong electric field. Collisions with the fill gas produce excited states (~11.6eV) that decay with the emission of a UV photon and electron-ion pairs (~26.4 eV for argon). The new electrons, plus the original, are accelerated to produce a cascade of ionization called "gas multiplication" or a Townsend avalanche. The multiplication factor for one avalanche is typically 106 to 108. Photons emitted can either directly ionize gas molecules or strike the cathode wall, liberating additional electrons that quickly produce additional avalanches at sites removed from the original. Thus a dense sheath of ionization propagates along the central wire in both directions, away from the region of initial excitation, producing what is termed a Geiger-Mueller discharge.

Figure 2. The mechanism by which additional avalanches are triggered in a Geiger-Mueller discharge.

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The intense electric field near the anode collects the electrons to the anode and repels the positive ions. Electron mobility is ~ 104 m/s or 104 times higher than that for positive ions. Electrons are collected within a few µs, while the sheath of massive positive ions (space charge) surrounding the center wire are accelerated much more slowly (ms) outward towards the cathode.

The temporary presence of a positive space charge surrounding the central anode terminates production of additional avalanches by reducing the field gradient near the center wire below the avalanche threshold. If ions reach the cathode with sufficient energy they can liberate new electrons, starting the process all over again, producing an endless continuous discharge that would render the detector useless. An early method for preventing this used external circuitry to "quench" the tube, but the introduction of organic or halogen vapors is now preferred. The complex molecule of the quenching vapor is selected to have a lower ionization potential ( < 10 eV) than that of the fill gas (26.4 eV). Upon collision with a vapor molecule the fill gas ion gives up ~ 10 eV to the quench vapor molecule which then quickly dissociates rather than losing its energy by radioactive emission. The remainder of the partially neutralized vapor-atom energy (~ 4 eV) produces a UV photon that is strongly absorbed by the molecules and prevented from reaching the cathode. Any quench vapor that might be accelerated and impact the cathode dissociates on contact. Organic quench vapors, such as alcohols, are permanently altered by this process, limiting tube life to ~ 109 counts. Halogen quench vapors dissociate in a reversible manner later recombining for an essentially infinite life.

Dead Time

The sheath of positive ions (space charge) close to the anode reduces the intense electric field sufficiently that approaching electrons do not gain sufficient energy to start new avalanches. The detector is then inoperative (dead) for the time required for the ion sheath to migrate outward far enough for the field gradient to recover above the avalanche threshold. The time required for recovery to a value high enough for a new pulse to be generated and counted is called the "dead time" and is of the order of 100 µs.

Measurement of Dead Time

Two Source Method:

Measuring the dead time of a system requires two sources, S1 and S2. A counting rate is measured first with S1, then S1 plus S2, and finally with only S2. If the dead time were zero the counting rate with both sources together would be simply the sum of the individual rates. The fact that it never is permits one to compute the actual dead time. At modest count rates this is straightforward. If the counting rates are very high it is necessary to decide which of two models applies, i.e., is the detector paralysable or non-paralysable.

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Oscilloscope:

The dead time of the GM tube may be directly determined with an oscilloscope by observing the recovery envelope of the pulses. Note carefully where the CRO is connected. The test point gives information about the GM tube only. Recovery must be sufficient to produce a pulse large enough to exceed the "threshold" of the following counting circuits. The "dead time" of these circuits should also be considered.

Correction of Count Rate to Include Dead Time:

If n' counts are recorded in a time interval t with a detector of dead time d, it is necessary to compute the true number n that would have been observed with a counter of zero dead time. Since n'd is the total dead time, and n/t is the true counting rate, (n/t) n'd is the total number of counts that would have occurred during the total dead time interval. Therefore (n/t) n'd = n - n'. In terms of the counting rate, R = n/t and R' = n'/t,

Pulse Size - Charge Collected:

The GM tube output is a charge pulse whose amplitude is independent of the energy of the detected radiation. The only amplitude information that it can provide is that the energy of the detected radiation was sufficient to produce electrons energetic enough to penetrate to the sensitive region of the tube. The quantity of charge produced is directly proportional to the "over voltage", i.e., the difference between the GM threshold voltage at which a GM discharge will first occur, and the higher normal operating voltage. The output signal will be directly proportional to the charge (108 - 1010 ion-pairs), and inversely proportional to the circuit capacitance (GM tube capacitance + the connecting cable capacitance + the input capacitance of the electronic system). The normal signal is of the order of volts.

Counting Statistics

The definitions for sample means, variances, and probability distribution with symbols are

Sample Mean:

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Sample Variance:

Gaussian distribution

Under the conditions that are thought to apply to all radioactive decays (i.e., all the nuclei are identical, independent, and each has a definite and constant probability of decay in a unit time interval), one can derive a distribution function P(x) that is the probability of observing x counts in one observation period.

The distribution of the values x about the true average µ is called the Gaussian distribution and has the form:

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The Meaning of Sigma:

If the mean of a Gaussian distribution becomes ~20, the distribution becomes symmetrical, assuming the characteristics of a Normal, or bell-shaped Gaussian distribution. This displays the characteristic that 68% of the total area of the distribution lies within ± sigma of the mean. For a Gaussian distribution sigma=sqrt(µ) , so that a counting measurement is 68% likely to be within ± sigma of the true population mean µ Since x is probably close to µ, we may take sigma = sqrt(x), and say that a single measurement is 68% likely to be within ± sqrt(x) of the true mean. Similarly the values for ± 2 sigma and ± 3 sigma are 95% and 99.7%, respectively. When plotting experimental results, it is customary to include error bars of length sigma1 on each point xi.

Examining a Gaussian distribution:

Use only "natural room background" radiation as a source with the GM tube in its lead "house". Take 0.5 minute runs and plot them on a histogram until the shape of the distribution emerges, or you have 20 runs. Counting at low rates for short time intervals (x < 20) produces the characteristically skewed Gaussian distribution.. Now calculate x-bar and s.

Methodology:

After setting the GM tube with timer scalar I put the radioactive source at the face of detector tube of GM counter at a distance of 3cm.By providing the ac source I switch on the apparatus and apply the threshold voltage to the timer scalar which is 420 volts. Then turn on the switch of counts ad take 30 readings with an interval of one minute without any break.

Tabulate these readings and found out the sample mean and sample variance of all readings. After this I found the standard derivation of both sample mean and variance. By taking class intervals I draw a curve of my data which shows the Gaussian distribution curve and calculate % error in σ.

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Observations and Calculations

Sr. # Time Activity x x-m (x-m)2

1 1 712 712 43.6 19002 2 1438 726 57.6 33183 3 2134 696 27.6 7624 4 2782 648 20.4 4165 5 3478 696 27.6 7626 6 4142 664 -4.4 197 7 4816 674 5.6 318 8 5443 627 -41.4 17149 9 6113 670 1.6 310 10 6746 633 -35.4 125311 11 7420 674 5.6 3112 12 8081 661 -7.4 5513 13 8775 694 25.6 65514 14 9467 692 23.6 55715 15 10147 680 11.6 13516 16 10791 644 -24.4 59517 17 11456 665 -3.4 1218 18 12132 676 7.6 5819 19 12805 673 4.6 2120 20 13463 658 -10.4 10821 21 14144 681 12.6 15922 22 14801 657 -11.4 13023 23 15502 701 32.6 106324 24 16100 599 -69.4 481625 25 16760 660 -8.4 7126 26 17378 618 -50.4 254027 27 18062 684 15.6 24328 28 18724 662 -6.4 4129 29 19370 646 -22.4 50230 30 20050 680 11.6 135

Now I draw the graph using

Along x-axis one small box = 3.2 ,Along y-axis one small box = 0.2

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Now finding standard deviation (S.D) from both graph and observations. Which is following

Sample mean (m= ):

=1/30(20051) =668.4

S.D from sample mean:

S.D=√668.4

=25.9=26

S.D from sample variance:

=1/30(22105) =736.83

s =√736.83=27.1=27

Now class interval:

C.I =Max- Min/8

=726-599/8=15.84=16

Sr # Class Interval Frequency1 599---615 12 615---631 23 631---647 34 647---663 65 663---679 76 679---695 67 695---711 38 711---726 2

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S.D from graph:

S.D = FWHD/1.8

=48/1.8=26.66

Where FWHD is full width half maximum, and it is always 70.7% of maximum frequency.

Now finding C.V from both observations and graph;

C.V from observation:

C.V = (S.D) (100)/mean

= (27) (100)/668.4

=4.04

C.V from graph:

C.V = (S.D) (100)/mean

= (26.66) (100)/668.4

=3.989 = 4

Calculate sigma:

Mean = max- min/2

= 726+599/2

=663

For ±σ;

Mean + S.D = 663+26.6 = 690

Mean - S.D = 663-26.6 = 637

From the table we have 19 readings in the class interval of 637---690.Thus

±σ = (19) (100)/30=63.33%

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For ±2σ;

Mean + S.D = 663+2(26.6) = 716

Mean – S.D = 663-2(26.6) = 610

From the table we have 28 readings in the class interval of 610---716.Thus

±2σ = (28) (100)/30 = 93.33%

For ±3σ;

Mean +S.D =663 +3(26.6) =743

Mean – S.D = 663-3(26.6) = 583

From the table we have 30 readings in the class interval of 583---743.Thus

±3σ = (30) (100)/30 = 100%

% Error:

% error in ±σ = 68.2%-63.33%= 4.87%

%error in ±2σ = 95.4%-93.33% = 2.07%

% error in ±3σ = 0%

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Source of errors and precautions:

The distance between GM tube and the source can disturb the experiment so it should be keep in mind that the this distance is always less than 6cm.

Resetting the timer scalar during performing the experiment do not give correct readings, so while perform the experiment do not reset the timer scalar.

Use the bars tube on the platform with as large a separation between the source and detector as permits the reasonable count rates.

The voltages applied to the timer scalar should not less than the threshold voltages.

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Questions and Answers

What amount of radiation is safe?

            Safe means free from danger or risk. Safer means more nearly free from risk than something else. Safest means the most nearly free from risk than other things under discussion. Even the safest car is not safe (risk-free). And even the smallest exposure to ionizing radiation is not safe (risk-free), with respect to cancer and inherited afflictions. In other words, there is no "threshold" dose-level below which all cancer-risk from radiation disappears.

            The amount of the danger or risk depends on the amount of radiation exposure. The only risk-free (safe) dose is zero-dose, with respect to unrepairable injury of chromosomes and DNA., by any reasonable standard of scientific proof. In 1993, the United Nations Scientific Committee on Effects of Atomic Radiation supported the same conclusion (UNSCEAR 1993). And in 1995, Britain's National Radiological Protection Board also concluded that the weight of the evidence "falls decisively in favor of" the no-threshold conclusion for benign and malignant tumors (NRPB 1995).

            When an individual receives a small extra dose of radiation, the person receives a small extra risk of cancer --- say, 1 chance in 1,000. The person has 999 chances out of 1,000 of escaping. But if 25,000,000 people like that individual each receive the same, small extra dose of radiation, each person receives 1 chance in 1,000. The consequence is a rate of 25,000 extra cancers in that group. Point:   A small personal risk can mean a large actual rate for a group --- a fact which produces important ethical and health issues.

Among the proven causes of human cancer, how important is radiation?

            We think that ionizing radiation is very probably the single most important human carcinogen of the 20th century. In 1997, CNR will publish a study which is consistent with that hypothesis.

            Other proven human carcinogens include certain viruses and chemical substances (including asbestos and tobacco smoke). Specific chemicals sometimes cause only specific types of cancer. By contrast, we predicted in 1969 that "All forms of cancer, in all probability, can be increased by radiation." This warning met with resistance from the radiation community, and we were called "controversial" (and worse). But by 1980, the radiation committee of the National Academy of Sciences acknowledged that "Cancer may be induced by radiation in nearly all the tissues of the human body"

            An extremely important question remains unsettled, however. Do the various carcinogens work synergistically (as co-factors, multiplying the potency of each other), or do they work additively (as independent agents having a fixed potency in every situation and in every nation)? We predict that they usually work as synergists. If correct, then reducing exposure to ionizing radiation --- which would be easy to do --- would also reduce the impact of many other carcinogens.

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Can one case of cancer have more than one cause?

            Most experts currently accept (a) the single-cell origin of a cancer and (b) the requirement for multiple genetic abnormalities in the same cell. It follows that a single case of cancer very probably has more than one cause, even if carcinogens act additively instead of synergistically.

            Suppose that a type of cancer requires the accumulation of 5 independent genetic injuries in the same cell. If only 4 occur, no cancer can occur. But each of the 5 injuries required (in this supposition) to produce one case of cancer, could be caused in the same cell by a different carcinogen. Some such injuries are surely inherited.

When you estimate that 75% of recent and current breast-cancer in the USA is due to earlier exposure to medical irradiation, do you mean that all other agents combined are responsible for only 25% of the cases?

            No, we don't. Our 75% incorporates a very big role for non-radiation agents, because it explicitly incorporates the assumption of synergy between them and radiation, with the other agents causing each unit of radiation to be much more potent in causing breast cancer in the USA than in Japan

How can radiation both be a cause of cancer and also be used to treat cancer?

            The "current wisdom" is that cancer begins with a single cell having abnormal genetic instructions. Over time, it (or one of its descendant cells) acquires additional injuries. Finally, a cell's abnormal instructions cause it to do abnormal things --- such as dividing too often, or forming a tumor, or migrating from its appropriate location to live and divide elsewhere in the body (metastasis). These cancerous activities are done by living cells, whose abnormalities can be caused by radiation.

            When radiation is used to treat cancer, it is used in very high doses which do enough damage to kill cells. Dead cells cannot behave like cancer. It is very difficult to give radiation only to cancer cells, without giving both high and low doses of radiation to healthy cells in the neighborhood. Methods in radiation therapy are improving with time.

Should people have radiation therapy to treat their cancer?

            We think informed consent is an important principle in medicine (and in every voluntary transaction).

            We hear from too many women with breast cancer whose own physicians told them only about the benefits from radiation therapy --- but not about the side-effects which sometimes occur on the irradiated side --- such as chronic swelling of the arm, chronic pain in the arm, paralysis of the arm (from radiation damage to its nerve), broken ribs (from radiation damage to bone), or radiation damage to the underlying lung or heart. Unavoidably, the non-cancerous breast also receives considerable radiation exposure.

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            Patients who consider radiation therapy for abdominal cancers may also want to ask for details about potential complications from radiation damage involving the bladder, intestines, ureters, kidneys, nerves, spine, etc.

Aren't some people more sensitive to radiation than the average person?

            Yes, almost certainly. But there is no way to identify them --- yet. For instance, several different genes provide every cell with the ability to repair routine injuries to chromosomes and DNA. People who are born with a faulty "repair gene" in every cell, are going to be more vulnerable than the average person to cancer induced by radiation and by other carcinogens (mutagens).

            When analysts study the cancer-response to radiation in human groups, the sensitive individuals are probably contributing much of the response. Therefore, the unlucky sensitive women are going to have higher risks from mammography than the average values in

and other women will have lower risks than indicated above.

Which is worse, external radiation or internal radiation?

            To a cell, all high-speed electrons feel alike, except for their particular energy (Introduction). A cell does not know why such electrons are there. And a cell does not care whether they come because of an external source (like an x-ray machine or a radium dial) or because of a radioactive substance inside you (for example, cesium-137, strontium-90, iodine-131). But the cell cares a lot about the number of such electrons, because (at equal energy per electron) the damage is proportional to the number.

            Unlike X-rays and gamma rays (photons), radioactive substances (radio-nuclides) have chemical properties, and the body uses them chemically. For instance, the body collects iodine in the thyroid gland. Therefore, thyroid cells experience many more high-speed electrons (and more damage) than do breast cells from internal radio-iodine.

How much extra radiation do we receive from flying?

            Radiation exposure, from natural cosmic sources, increases with altitude, with peak dose at about 45,000 feet. Dose from cosmic radiation also varies with latitude;   it is lowest near the equator and highest near the poles. Therefore, the extra radiation dose from flying depends on (a) the particular route, (b) the duration of the flight, and (c) the fraction of the trip spent below the flight's maximum altitude.

            A useful "ballpark" value for a nonstop commercial flight, from California to New York and back, is an extra dose to all your organs of about 0.003 rem (3 milli-rems). Such a trip adds about 3% to the average annual whole-body dose from all natural radiation combined --- which is about 100 milli-rems per year of whole-body exposure in the USA, on the average.

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Why do some sources say our average dose from natural background is 100 milli-rems per year, and other sources say the dose is 250 milli-rems or more? Who's right?

            There is no contradiction. There is just some carelessness in specifying what each number describes.

            100 milli-rems per year refers to the average annual whole-body exposure. Every organ is at risk, including the ovaries and testes. The figure of 100 milli-rems per year excludes exposure by natural radon and thoron because these radio-nuclides and their radioactive decay-products cause primarily lung-exposure, rather than primarily whole-body exposure.

            250 milli-rems of annual effective dose equivalent is a number which combines the whole-body exposure with the partial-body exposure --- by applying a long series of assumptions about the relative importance of each organ, in terms of health consequences.

Rads, rems, grays, sieverts, effective dose equivalents, roentgens --- how can we cope with such terms?

            The rad is the most "solid" unit of biological dose, because it contains no assumptions. A rad is defined as a certain amount of energy deposited by high-speed particles per gram of biological tissue .Rads and roentgens are almost equivalent. The gray is the name for 100 rads.

            The rem is a unit which incorporates some evidence and some assumptions about the relative harmfulness of various high-speed particles, even when they deliver the same amount of energy per gram of biological tissue. In general, the rad and the rem are equivalent only when discussing gamma rays (or certain xrays). The sievert is the name for 100 rems.

            The effective dose equivalent, which is always expressed in rems or sieverts, incorporates many additional assumptions about biological consequences "Effective doses" and rad-doses are not directly comparable.

How much extra radiation dose do I get from a smoke detector?

            Very, very little. If you have a photo-electric smoke detector, there is no radioactive substance in it. If you have the much more common "ionization" type, there is a radio-nuclide in it --- usually 1 micro-curie of americium-241. A micro-curie is one-millionth of one curie. Americium-241 emits alpha particles, which are kept inside the case. It also emits some gamma radiation which can penetrate the case. We measured the gamma dose-rate from our own smoke detector, and 3 feet away from it, the extra dose-rate was 1/80 of a micro-rad per hour --- 1/80 of one millionth of a rad. To receive one

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extra milli-rad of gamma dose from our detector, we would have to sit 3 feet away from it for about 80,000 hours.

Which is more dangerous --- a radioactive substance with a short half-life or a long half-life?

            Two opposite answers are possible!   To understand why, one must consider the very simple --- but amazing --- law of radioactive decay, which is:   The fraction of atoms (of a pure radio-nuclide) decaying per unit of time equals 0.693 divided by the radioactive half-life. If the half-life is expressed in years, then the fraction decaying is "per year."

  The radioactive half-life of plutonium-239 is about 24,400 years, compared with about 88 years for plutonium-238. The way their atoms decay is comparable:   Each atom ejects (out of its nucleus) a high-speed alpha particle having over 5 million electron-volts of energy. An alpha particle consists of 2 protons plus 2 neutrons;   the particle carries a +2 electrical charge;   it interacts so fiercely with tissue that it "spends" all of its kinetic energy within just a few cells.

            Is it more dangerous to have 100,000 atoms of Pu-239 in your body, or 100,000 atoms of Pu-238?

            The fraction of Pu-239 atoms decaying per year = 0.693 / 24,400 years = 0.000028402. So, during the first year, the number of atoms decaying = 100,000 atoms times 0.000028402 = 2.8 atoms. Since there are no fractional atoms, we'll say 3 atoms. The fraction of Pu-238 atoms decaying per year = 0.693 / 88 years = 0.007875. So, during the first year, the number of atoms decaying = 100,000 atoms times 0.007875 = 788 atoms --- lots more than 3.

            During the second year, the decayed atoms are no longer available to decay. So the number of Pu-239 atoms decaying = 99,997 available atoms x 0.000028402 = 2.84 atoms, or 3 again. The number of Pu-238 atoms decaying = 99,212 atoms x 0.007875 = 781 atoms --- still lots more than 3.

            Since the biological damage per year is proportional to the number of decaying atoms, the Pu-238 will remain much more dangerous, if you start with equal numbers of atoms.

            by contrast, the Pu-239 will do slightly more damage than the Pu-238, if you start with equal curies --- or partial curies (e.g., a nano-curie:   "only" 37 decays per second).

            Many more atoms of Pu-239 than Pu-238 are required to produce an equal number of decays per second. Why? The fraction of Pu-238 atoms decaying per unit time is about 277 times larger than the fraction of Pu-239 atoms decaying per unit time. An example of equal decays from unequal number of atoms:   (1,000,000 Pu-238 atoms) x

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(0.007875) = 7,875 decays during first year. And:   (277,000,000 Pu-239 atoms) x (0.000028402) = 7,867 decays during first year --- the same.

            Initially equal curies of Pu-239 and of Pu-238 cause equal decays (equal damage) during the first year. But during every subsequent year, the remaining Pu-238 atoms eject fewer alpha particles per year than the remaining Pu-239 atoms. That is because a smaller fraction remains of the original Pu-238 atoms than the original Pu-239 atoms. The ratio of remaining atoms is no longer 277. This being the case, the two samples cannot continue to generate equal decays per year, as they did at the outset. Pu-239 generates more than Pu-238.

            In diagnostic nuclear medicine, radio-nuclides are measured in fractional curies. With initially equal curies of two nuclides having comparable biochemical behavior, shorter half-life means less radiation dose than longer half-life.

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Glossary of Nuclear Science Terms

 

A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z

- A -

Absorber Any material that stops ionizing radiation. Lead, concrete, and steel attenuate gamma rays. A thin sheet of paper or metal will stop or absorb alpha particles and most beta particles.

Alpha particle (alpha radiation, alpha ray) A positively charged particle (a Helium-4 nucleus) made up of two neutrons and two protons. It is the least penetrating of the three common forms of radiation, being stopped by a sheet of paper. It is not dangerous to living things unless the alpha-emitting substance is inhaled or ingested or comes into contact with the lens of the eye.

Atom A particle of matter indivisible by chemical means. It is the fundamental building block of elements.

Atomic number The number assigned to each element on the basis of the number of protons found in the element's nucleus.

Atomic weight (atomic mass) Approximately the sum of the number of protons and neutrons found in the nucleus of an atom.

- B -

Background radiation The radiation of man's natural environment originating primarily from the naturally radioactive elements of the earth and from the cosmic rays. The term may also mean radiation extraneous to an experiment.

Beta particle (beta radiation, beta ray) An electron of either positive charge (ß+) or negative charge (ß-), which has been emitted by an atomic nucleus or neutron in the process of a transformation. Beta particles are more penetrating than alpha particles but less than gamma rays or x-rays.

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- C -

Contamination Radioactive material deposited or dispersed in materials or places where it is not wanted.

Cow A radioisotope generator system.

Curie (Ci) The basic unit used to describe the intensity of radioactivity in a sample of material. One curie equals thirty-seven billion disintegrations per second, or approximately the radioactivity of one gram of radium.

- D -

Daughter A nucleus formed by the radioactive decay of a different (parent) nuclide.

Decay (radioactive) The change of one radioactive nuclide into a different nuclide by the spontaneous emission of alpha, beta, or gamma rays, or by electron capture. The end product is a less energetic, more stable nucleus. Each decay process has a definite half-life.

Decontamination The removal of radioactive contaminants by cleaning and washing with chemicals.

Density That property of a substance which is expressed by the ratio of its mass to its volume.

Dose A general term denoting the quantity of radiation or energy absorbed in a specific mass.

- E -

Electromagnetic radiation Radiation consisting of electric and magnetic waves that travel at the speed of light. Examples: light, radio waves, gamma rays, x-rays.

Electron An elementary particle with a unit electrical charge and a mass 1/1837 that of the proton. Electrons surround the atom's positively charged nucleus and determine the atom's chemical properties.

Electron capture A radioactive decay process in which an orbital electron is captured by and merges with the nucleus. The mass number is unchanged, but the atomic number is decreased by one.

Eluant Washing solution (The solution that is introduced into the cow).

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Eluate The washings obtained by elution (the solution that comes out of the cow).

Elute To separate by washing (to milk).

Excited state The state of an atom or nucleus when it possesses more than its normal energy. The excess energy is usually released eventually as a gamma ray.

- F -

Fission The splitting of a heavy nucleus into two roughly equal parts (which are nuclei of lighter elements), accompanied by the release of a relatively large amount of energy in the form of kinetic energy of the two parts and in the form of emission of neutrons and gamma rays.

Fission products Nuclei formed by the fission of heavy elements. They are of medium atomic weight and almost all are radioactive. Examples: strontium-90, cesium-137.

- G -

Gamma ray A highly penetrating type of nuclear radiation, similar to x-radiation, except that it comes from within the nucleus of an atom, and, in general, has a shorter wavelength.

Geiger counter A Geiger-Müller detector and measuring instrument. It contains a gas-filled tube which discharges electrically when ionizing radiation passes through it and a device that records the events.

Generator A cow-a system containing a parent-daughter set of radioisotopes in which the parent decays through a daughter to a stable isotope. The daughter is a different element from that of the parent, and, hence, can be separated from the parent by elution (milking).

- H -

Half-life The time in which half the atoms of a particular radioactive nuclide disintegrate. The half-life is a characteristic property of each radioactive isotope.

Health physics That science devoted to recognition, evaluation, and control of all health hazards from ionizing radiation.

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- I -

Induced radioactivity Radioactivity that is created by bombarding a substance with neutrons in a reactor or with charged particles produced by particle accelerators.

Ion An atomic particle that is electrically charged, either negative or positive.

Ionizing radiation Radiation that is capable of producing ions either directly or indirectly.

Irradiate To expose to some form of radiation.

Isomer One of several nuclides with the same number of neutrons and protons capable of existing for a measurable time in different nuclear energy states.

Isometric transition A mode of radioactive decay where a nucleus goes from a higher to a lower energy state. The mass number and the atomic number are unchanged.

Isotope Isotopes of a given element have the same atomic number (same number of protons in their nuclei) but different atomic weights (different number of neutrons in their nuclei). Uranium-238 and uranium-235 are isotopes of uranium.

- K -

K-capture The capture by an atom's nucleus of an orbital electron from the first K-shell surrounding the nucleus.

keV One thousand electron volts.

- L -

- M -

MeV One million electron volts.

Microcurie (µCi) One millionth of a curie (3.7 x 104 disintegrations per second).

Milk To elute a cow.

Minigenerator A trademark of Union Carbide Corporation that is used to identify radioisotope generator systems for educational use.

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- N -

Neutrino An electrically neutral particle with negligible mass. It is produced in many nuclear reactions such as in beta decay.

Neutron One of the basic particles which make up an atom. A neutron and a proton have about the same weight, but the neutron has no electrical charge.

Nuclear reactor A device in which a fission chain reaction can be initiated, maintained, and controlled. Its essential components are fissionable fuel, moderator, shielding, control rods, and coolant.

Nucleon A constituent of the nucleus; that is, a proton or a neutron.

Nucleonics The science, technology, and application of nuclear energy.

Nucleus The core of the atom, where most of its mass and all of its positive charge is concentrated. Except for hydrogen, it consists of protons and neutrons.

Nuclide Any species of atom that exists for a measurable length of time. A nuclide can be distinguished by its atomic weight, atomic number, and energy state.

- O -

- P -

Parent A radionuclide that decays to another nuclide which may be either radioactive or stable.

Photon A quantity of electromagnetic energy. Photons have momentum but no mass or electrical charge.

Proton One of the basic particles which makes up an atom. The proton is found in the nucleus and has a positive electrical charge equivalent to the negative charge of an electron and a mass similar to that of a neutron: a hydrogen nucleus.

- Q -

- R -

Rad Radiation Absorbed Dose. The basic unit of an absorbed dose of ionizing radiation. One rad is equal to the absorption of 100 ergs of radiation energy per gram of matter.

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Radioactive dating A technique for estimating the age of an object by measuring the amounts of various radioisotopes in it.

Radioactive waste Materials which are radioactive and for which there is no further use.

Radioactivity The spontaneous decay of disintegration of an unstable atomic nucleus accompanied by the emission of radiation.

Radioisotope A radioactive isotope. A common term for a radionuclide.

Radionuclide A radioactive nuclide. An unstable isotope of an element that decays or disintegrates spontaneously, emitting radiation.

Rate meter An electronic instrument that indicates, on a meter, the number of radiation induced pulses per minute from radiation detectors such as a Geiger-Muller tube.

- S -

Scaler An electronic instrument for counting radiation induced pulses from radiation detectors such as a Geiger-Muller tube.

Scintillation counter An instrument that detects and measures gamma radiation by counting the light flashes (scintillations) induced by the radiation.

Secular equilibrium A state of parent-daughter equilibrium which is achieved when the half-life of the parent is much longer than the half-life of the daughter. In this case, if the two are not separated, the daughter will eventually be decaying at the same rate at which it is being produced. At this point, both parent and daughter will decay at the same rate until the parent is essentially exhausted.

Shielding A protective barrier, usually a dense material, which reduces the passage of radiation from radioactive materials to the surroundings.

Source A radioactive material that produces radiation for experimental or industrial use.

Spill The accidental release of radioactive materials.

Stable Non-radioactive.

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- T -

Tracer A small amount of radioactive isotope introduced into a system in order to follow the behavior of some component of that system.

Transmutation The transformation of one element into another by a nuclear reaction.

- UVWXYZ -

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