Physics 115B Lab 1: Energy, Temperature, Heat, and Power

Part I: Thermometers from many lands There is a collection of thermometers on the table, including an

unusual Star-Trekky one (the “grey instrument”, “g.i.”) several digital thermometers, some hooked up to computers. 1. Pick up the g.i., study it, play with it, and see if you can figure

out how to use it. 2. Use it on yourself (or a partner), on the wall, on a computer

screen, and at least four other interesting items. Make a table in your notebook showing the results. If you find especially interesting uses or outcomes, record them.

3. Shine the red lamp on the mirror at about a 45º angle. Use the g.i. to measure the bulb temperature. Then use it to measure the temperature of the mirror on the reflection of the bulb. Is the mirror really that hot? Discuss how the g.i. might work, and put some speculations in your notebook.

4. Fill a beaker of water and use each of the thermometers (including the g.i. and a computer one) on the water. Record your results in a table in your notebook. Does the temperature change if you briefly stir the water?

5. Put your hands around the beaker and repeat Step 4 with the computer thermometer. Is the energy of the water changing? Why? Does the temperature change if you stir briefly?

6. Describe in one paragraph some real-world situations where the g.i. would be useful. Describe cases in which it would be inaccurate.

7. (If there is time.) Look at the decorative thermometer. Can you make it change? Discuss how it might work and put some speculations in your notebook.

Part II: Liquid Nitrogen Demos The AI’s will show you cool things with serious cold!!

Part III: Transforming Kinetic Energy to Heat Energy 1. Carefully open the bottle and see what is inside. Measure the

temperature inside using digital thermometer. Make sure the thermometer doesn’t touch the bottom of the plastic bottle. Leave the thermometer in place to see how long the temperature takes to stabilize.

2. Describe in energy terms what would happen if you shook the bottle vigorously and then set it down. Would the energy content of the bottle change? What about the temperature? What if you waited awhile afterword?

3. Put the lid on the bottle and shake it 40 times vigorously. Repeat your temperature measurement. Watch it for a while. Record what you observe, then graph the result. Try repeating the experiment several times. Compare what you observe to your expectation in Step 2.

4. There is a big brass object attached to the table. On top of it, there is a slot, where you can insert a digital thermometer and measure its temperature. Using the friction with a belt, try to increase its temperature by 2°C. Do you have more respect for heat energy now?

Part IV: Heat and Temperature Using the materials available on the table, we’ll take a look at

how objects store heat. In order to get this accurately, you’ll need to make some careful measurements and record the data in your notebook. You will follow the steps listed below. Read the steps now, but, before you do them, read the rest of this section. You should understand exactly how the steps will allow you to determine the specific heat of your sample before you start making the measurements. 1. Chose a metal block and measure its mass (Mmetal). (Different

groups should choose different samples.) Also measure the mass of an empty styrofoam cup.

2. Fill the beaker with cold water and ice. You’ll find those in the fridge/freezer.

3. Put tap water in a styrofoam cup and measure its total mass. From that determine the mass of the water (MH20). There should be just enough water in the cup just to have your block completely submerged. Measure its temperature without the block (TH20,intial). You can use two probes on the same computer, one for the ice water, one for the tap water.

4. Attach a string to the metal sample and put it in the ice water. Measure the temperature of the water (Tice water =Tmetal,initial).

5. Then, carefully place the metal sample in the styrofoam cup of water. Stir and track the temperature on the computer. When it reaches a constant value, record it: (TH20,final=Tmetal,final). We can connect the temperature change of the water to energy.

Recall from your textbook that the heat (energy) required to raise the temperature of 1 kg of water by 1°C is 1 Calorie ≈ 4200 J, so it takes about 4.2 J to raise 1 g of water by 1°C. How much did the temperature of the water in the styrofoam cup change when the block was added? How many Joules of heat energy did the water lose? What principle allows you to determine the change in the

energy of the block? By how much did its energy change? Did its temperature change by the same amount as the water?

Temperature and heat are related, but not the same! Each substance has a “specific heat,” the amount of energy needed to raise 1 g of the substance by 1°C. From the above discussion, the specific heat of water is CH2O ≈ 4.2 J/g-°C. (It can also be quoted in other units, for example, 1 Cal/kg-°C.) C does not depend on the mass, shape, or temperature of the material – it just depends on what the object is made of.

Use this definition and your measurements to figure out the specific heat, Cmetal, for your block. Report your result to one of the AI’s – we will compare the values for the different metals measured by the different groups in all the labs. Does your metal or water have the higher specific heat?

Discuss and list some real-world situations when having a material with high specific heat or low specific heat can be important.

Part V: Electrical Energy and Power – a Watt is a Watt The 100-Watt light bulb has been set up for safe immersion in

water. (Don’t try this at home!) 1. First try plugging it into the Kill-A-Watt meter. Try the various

buttons. How much electrical power is being used? We will try to measure this ourselves.

2. Put enough tap water in the plastic water jug to cover the bulb. 500 ml should do it. Figure out the mass of the water. (Why is it easy if you used 500 ml?) Put the probe of a digital thermometer in the water. It should not touch the wall of the jug or the bulb. Use a plastic ruler to stir the water gently. Measure the temperature of the water with the bulb off.

3. Turn on the bulb. Record the temperature at fixed time intervals, say every 30 seconds, for several minutes. Stir the water gently and continuously with the ruler. Plot the temperature vs. time.

4. We can connect the temperature change of the water to energy. Recall from your textbook that the heat (energy) required to raise the temperature of 1 kg of water by 1°C is 1 Calorie ≈ 4200 J, so it takes about 4.2 J to raise 1 g of water by 1°C. At what rate is energy being added to the water (J/s = Watts) while the bulb is on?

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Physics 115B Lab 2: Atoms, molecules, and measuring the

very small In this lab we will make a series of measurements using simple

equipment (rulers, beakers, lab balances) that will give us estimates of molecular-scale quantities such as the size of a molecule, the wavelength of light, and Avogadro’s number.

Warm-up 1: Guesses Do this exercise individually, without consulting lab partners or

other sources. You won’t be judged (or graded) on the accuracy of your results – this is for later comparison with what you’ll measure in today’s lab.

1. In your notebook, rank in order of increasing size the following items:

• The wavelength of visible light • The diameter of an atom • The length of a molecule. We’ll be using an oil (oleic acid)

with chemical formula C18H34O2, that forms a long chain of atoms, so use that in your thinking. Here’s a model:

(Wikipedia, Oleic Acid)

• The average distance between molecules in air 2. Guess numbers for the sizes, indicating both a guess for the

size of each item and the ratios between adjacent sizes in your list. (Example: you might guess that an atom is 25 times larger than the wavelength of light.)

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Warm-up 2: Slick You know that oil floats on water, and, at least since the Gulf

oil spill, you know that oil on water forms a “slick” – a very thin layer or film. Under controlled circumstances, this film can be one molecule thick! (So an oil spill spreads very far indeed.) It isn’t easy to prove that the layer is one molecule thick, but, by assuming this, we can measure the size (it turns out to be roughly the length) of an oil molecule, something Lord Rayleigh did in 1890. Though there are some practical issues, the concept couldn’t be simpler.

• Figure out how to determine the thickness t of the film formed by a volume of oil V by measuring the area of the film A.

We make the patch of oil visible by dusting a bit of the surface of the water with baby powder. The AIs will demonstrate this. They will also suggest some assumptions we are making and maybe test them.

Parts I, II, and III can be done in any order – the AIs will get your group started on one after the demo, then move on to the others. Don’t forget Part IV at the end.

Both Parts I and II will need you to measure the volume of a drop from an eyedropper. We will assume that all the droppers are the same (we tried a few, and they are at least similar), so your group need only measure one dropper. Do this as part of Part I or II, whichever your group does first, as the graduated cylinders are available.

• Using water and one of the 25-ml graduated cylinders, determine the volume of one drop from your eyedropper. Each group member should try this, using the same dropper.

Part I: Measuring the size of a molecule with a ruler The trick now is to make this quantitative, and what makes it

hard is that V must be known and must be quite small to keep the

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film smaller than our pans. (Rayleigh used a very large pan; Ben Franklin, who started all this, publishing an account in 1774, used a pond.) As part of the Warm-up 2 demo, the AIs will make a 1:1000 mixture of oil:water. Oil and water, famously, do not mix, but we can do well enough by making a suspension of tiny oil droplets. When you put a drop of the mix in your pan of water, the water in the mix will just enter the water in the pan, leaving the oil droplets to join and form the film.

• Make several measurements of areas of films, each from a single drop, in the pans, recording the results. (You may only get to do one trial per pan. Let the AIs know if you need to reuse a pan – they can help dump it out and clean it for another trial.)

• Estimate the size of a molecule of the oil, assuming that the film is one molecule thick. Remember that your drop was not all oil!

• Assuming that all the measurements you have made are accurate, what effects could make your estimate of the molecular size too big? too small?

• From the size of a molecule, estimate the number of oil molecules in a cubic centimeter of oil. This is called the number density, n. To do this, you need to make assumptions about the shape of an oil molecule. Assume that the molecules are cubes that are packed together. (This turns out to be a poor assumption – see the picture on page 1 – but it will do for now.) You can (and should) calculate the number of oil molecules in your film. It is surprising that you can measure such a number (even roughly) so simply!

• For the next steps, we will need the density (mass per cubic centimeter) of the oil. The AI’s have some oil you can use to measure this. Give the oil back to them when you are done.

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The oil we are using is oleic acid, the major component of olive oil. (Rayleigh and Franklin just used olive oil.) Oleic acid is described by the chemical formulas C18H34O2 or CH3 (CH2)7 CH = CH (CH2)7 COOH . The important constant Avogadro’s number, NA, is the number of atoms or molecules of a substance in a mole of that substance. The atomic or molecular weight is the mass in grams of a mole of atoms or molecules of a given type. The atomic weights of hydrogen, carbon, and oxygen are 1, 12, and 16, respectively, so, for example, a mole of carbon atoms has a mass of 12 g.

• From this information, what is the molecular weight of oleic acid?

• Using this molecular weight and your measurements, calculate an estimate of NA, Avogadro’s number.

• Discuss factors that could cause your estimate to vary from the accepted value, NA = 6.02×1023 molecules/mole.∗

Note from the right-hand chemical formula above and the picture on page 1 that oleic acid is a chain of carbon and oxygen about 20 atoms long. (The structure is a bit bent, but we’ll ignore that.)

• From your measurements, what is the diameter of an atom?

∗ We often ask questions like this, and it is worth noting what we are looking for.

We are not looking for “I could have forgotten a term in my equation.” or “I could have multiplied wrong.” or “I could have weighed the sample wrong.” Even though we call this exercise “understanding the errors,” that does not mean mistakes. We are looking for specific effects or inaccurate assumptions (explicit or hidden) that could have distorted a measurement or its interpretation. An example from this lab would be assumptions about the shape of an oil molecule. An example from last week would be the assumption that no heat was lost through the wall of a beaker. You should not only list such effects, but indicate, if possible, the direction they would change your result. For example: “Not taking into account the heat entering through the wall of the beaker during the measurement would make our measured specific heat too small.”

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Part II: The wavelength of light As we will study later in the course, light is an electromagnetic

wave. No matter is moving in this wave – what is oscillating as the wave propagates is the strength of electric and magnetic fields. Though this is very abstract, our usual picture of a wave applies, but with a different meaning of the graph.

Instead of the graph representing, say, the height of the water

surface in an ocean wave, it can be the strength of the electric field. A stationary observer would measure the electric field getting stronger and weaker as the wave went by, just as a person in the ocean would bob up and down as a water wave passed.

Like any sine wave, this wave has a wavelength, the distance between two adjacent crests or troughs, for which we use the Greek letter lambda, λ. We can ask, If light is a wave, what is its wavelength? You may know that the wavelength of light depends on its color. Since we just want an order-of-magnitude estimate, this won’t matter to us (though it will make the patterns we observe quite beautiful.)

• Dip a wire-loop in the bubble solution. Go ahead – blow a bubble or two! Look specifically at the reflections of the room lights, noting that the reflections are pretty colors, not the white of the lights themselves. We can make the pattern of colors more regular. Dip the loop again. This time hold it so the loop is vertical and look at the reflections in the flat bubble spanning the loop. Note that there are horizontal

whole pattern moves

wavelength λ

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bands of alternating green and red. The pattern moves as the water drains downward, making the film thinner. Eventually, there is no reflection at all from the top, even though the bubble hasn’t popped yet (though it is about to.) Each member of the group should make and observe this pattern.

As we’ll learn when we study waves later in the course, the bands of color appear when the film is about a wavelength thick, via a process called interference. In fact, for a color with wavelength λ, when the film is ¼×λ, ¾×λ, 5/4×λ,... thick you see a bright reflection of that color. Because gravity drains the water downward, the bubble in the loop is thinner at the top and thicker at the bottom, and there are horizontal bands of constant thickness. This means the green and red reflections alternate as each color goes through the multiples of its λ. As the water drains, the pattern shifts downward. Eventually, the top of the bubble is less than ¼-wavelength thick and there is no color that reflects, that is, no reflection at all. For our purposes, we just need the fact that when there are a few bands present, the film is about a wavelength thick.

To make this quantitative, we will use a variant of the same trick used in Part I. In this part, we use turpentine. We use turpentine because, for some reason, it forms films that show interference bands. This tells us the film is about a wavelength thick, even if we don’t know why that happens. Note that, unlike the oil we use in Part I, the turpentine evaporates quite rapidly. This means that there is some uncertainty about the volume of oil remaining. On the plus side, it means we can try several drops in succession in the same pan without dumping it and restarting.

To make our measurements of the wavelength of light, we will drop one drop of turpentine into a tray of water. To know the film thickness is about a wavelength, we need to see the colored reflection bands. Before using the turpentine, look at the reflection of a light in the room (a lamp or one on the ceiling) in the water. Note that the reflection is white. If you make sure the reflected

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image of a light is on your film of turpentine, you can look for the colors. You can try dropping the drops with or without using a patch of baby powder. Even without it, you can see the edge of the film of turpentine on the water.

• Make observations of what happens when you put a drop of turpentine on the water. Make sketches of what you see or describe it in words. We have always seen one oddity: the first drop spreads to cover the whole tray, but subsequent drops make near-circular films of reasonable size. Measure the diameters of all films after the first. Note roughly how long after the drop you see the colors, when they vanish, and when the film itself vanishes. We found that you can do five or six drops in the pan before it gets too messy.

• Estimate the wavelength of light using your observations and measurements.

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Part III: Weighing air It seems odd, but it turns out to be easy to weigh air. Your

equipment: a flask with a valve, a balance, and a vacuum pump. The pump can suck just about all the air out of the flask in about a minute. (The flasks have a protective coating and are glued inside the boxes for safety.) Note the valve with the black handle on the flask. It is open when the handle points straight out from the stem.

• Figure out how to find the mass of air in the flask and do it – record the result. Pretty easy. Do it again (have each group member try it) to see if you get the same result. What would happen if you tried to weigh helium this way?

• Use your result to find the density (g/cm3) of air. What do you need to do this? Figure this out with the tools at hand.

Air is mostly nitrogen molecules, N2. (For simplicity, we’ll assume it is all nitrogen. The oxygen molecules have about the same mass, so this is a fine approximation.) The molecular weight of nitrogen is 28, so one mole of N2 has a mass of 28 g. In Part I, you determine the number of molecules in a mole, called Avogadro’s number, from measurements you made. Don’t worry if you haven’t done Part I yet – we’ll use the actual value, NA = 6.02×1023 molecules/mole, here.

• From your measured density of air, the molecular weight of N2, and the value of NA, find the number density, that is, the number of molecules per cm3 of air.

• Now figure out the average distance between air molecules. This will take some thinking and discussion in your group. Indicate your reasoning in your notebook.

Part IV: Summary Remake the same list from Warm-up 1, using the results of this

lab, including the sizes and ratios from your measurements.

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Physics 115B Lab 3: Motion

Part I: Catch the ball On the table is a track on which a cart can roll with little

friction. The top section of the cart is a launcher that shoots a ball straight up. Ask an AI to show you how to activate the launcher. Never stand with your face directly above the launcher – it can fire without warning!!! There is also an adjustable spring that can give the cart a reproducible velocity along the track.

• Determine how high the ball goes when launched with the cart at rest. This takes at least two people: one to trigger the launcher and hold the meter stick, and one or more to watch how high the ball goes. Do quite a few trials with each member of your group launching and watching the height. Everyone should have a record of all the launches. Look for reproducibility in two forms: precision, how close in height are the launches? are there outliers, occasional misfires that go to a quite different height? Also, be sure to decide what you should define as the initial height of the ball.

At this point, ask the AI to take the ball away. Ask your AI to demonstrate the cart-launching spring and how to adjust it. • You will use a light gate (an LED light source and light

sensor that straddle the track and a timer) to measure the cart’s speed just before it launches the ball. You shouldn’t have to do anything to the timer other than turning it on (power switch on the back) and hitting the reset button on the front. Figure out how this system works. (Try passing your hand between the LED and the sensor. What happens?) How can you use this setup to measure the speed of the cart?

• Choose a setting of the spring and record it in your notebook. Without launching the ball, launch the cart

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several times, again looking for reproducibility in both forms.

• Knowing the velocity of the cart and the height the ball reaches, compute the location where the ball will land (see formula below). Place the cup at that location, making sure the bumper is between the ball-launch point and the cup.

Call the AI over. He’ll give the ball back and observe. • Launch the cart with the ball-launcher armed. If the ball is

caught in the cup, congratulations! Try it again. If not, check the calculations and the velocity and try again.

• Now remove the cup, move the bumper to the far end of the track and try a few more launches. Vary the cart speed by adjusting the spring. What do you observe? (No numbers needed, just watch.) Why does it make sense?

Useful formula: The time it takes an object to fall a height h starting at rest is

ght fall

2= ,

where g is the gravitational acceleration, g = 9.8 m/s2 = 980 cm/s2. (If you know how to derive this result, show your lab partners, but for this lab we will take it as given.) Figure out how to use this formula in your calculation of where to put the cup. Show your reasoning and all calculations in your notebook.

The Big Picture: this is the essence of Newtonian determinism, discussed in lecture. Given the initial position and velocity of an object and knowledge of the forces, the object’s future position is completely predictable. Where in your calculation did you express the knowledge of the forces?

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Part II: Spinning toys This lab will be our only look at things that spin. We’ll mostly

just ask that you observe, but we do want you to realize that conservation of energy and, as we will see in Part III, a new quantity called angular momentum, are universal.

The toys in this section fall into three categories. • Category 1: spin the “Top secret top,” the little silver top on

the round black stand. Start the “Space wheel,” the little satellite thingy by putting it on its stand (the two vertical transparent plates on a black stand) near one end and letting go. Just do each one once and let them do their thing while you go on to the other toys.

• Category 2: Before the first spins, guess how long each toy will spin. Take turns spinning the “Quark top” and the “Euler disk” on their mirrors. (The mirrors are just smooth surfaces.) Time how long each spins. To set the Euler disk going, you place on edge at a slight angle (tilted on the edge that that is rounder; the sharper edge tends to scratch the surface) on its mirror (the slightly concave one). If you give it a good spin it will spin like a coin. Record in your notebook interesting things you observe with the Euler disk as it comes to rest.

• Category 3: There are three similar tops, two half-green wooden ones and one orange green plastic one, that do something odd. (Have an AI show you how to work the plastic top on the plastic top.) What is odd about this behavior? What must be true for this to be consistent with conservation of energy? Though the sippy birds are not spinning, their iconic behavior is odd. What provides the energy needed for them to keep going despite friction?

• Now look back at the Category 1 toys. Can they actually be frictionless? What if we told you (truthfully) that they’d

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keep going for days? What would you suspect was going on? (Hint: aren’t the bases a bit heavy?)

Part III: Angular momentum (and more toys) • If you are uncomfortable trying this, do it very slowly

and/or ask an AI to help you. You must be careful – if you spin too fast you can hurt yourself by falling off or someone else by hitting them, especially when you get dizzy! Sit on the blue stool. Sit upright (don’t lean in any direction), with you arms extended horizontally to the sides. Push yourself with your feet, or have a lab partner push your arm so you turn slowly. When you are turning steadily, bring you hands in to your chest. What happens to your rate of spin? Put your arms back out. What happens? Everyone should try this – if you are nervous, do it in the reverse order, starting with your arms in. This will be quite tame. You can try this with the dumbbells in your hands. If you do, start with arms in.

• Sit on the stool again. Have a partner spin up the bicycle wheel as fast as possible (note that this one is meant to turn only in one direction). Have him/her hand the wheel to you with the axle oriented vertically. With the stool at rest and with you holding the axle firmly at both ends, turn the wheel over, so that the axle that was on the bottom is now on the top. What happens?

• Spin the wheel with the axle horizontal. Try to turn the wheel as if you were steering it for a left turn, keeping it upright. Hold the axles tightly, but let your arms respond to what the wheel does.

Find an AI and describe your observations to him. We will try to extract the properties of a new quantity called angular momentum from your observations.

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• Find the colored plastic oblongs. Try spinning them on a table, first clockwise, then counter-clockwise. Why is this behavior odd? Does it violate the law of conservation of angular momentum? Why or why not?

• Just for fun: turn over the pair of connected bottles to see the tornado. Spin the water-filled gyroscope.

• Find the book held closed by the rubber band. Try flipping it in the air about each of its three axes of symmetry. What do you observe? This odd behavior is universal and well understood from Newton’s Laws.

Part IV: Air An AI will do a demonstration in which the big vacuum cleaner

can support a ball on its air jet. What must the direction of the net force of the air on the ball be?

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Physics 115B Lab 4: Radioactivity

In this lab, we will study radioactivity. Chapter 4 of your textbook is a good introduction, to the physics and the terminology, but also to the effects of radiation. You probably know a bit, and you will learn more in this course, about the technological, political, and health impacts of radioactivity. From a scientific and philosophical point of view, however, radioactivity and radiation are a direct, observable connection to the atomic and sub-atomic world.

Though some of the sources of radioactivity we will use are created for scientific purposes, several are from the grocery store or the hardware store and are found in almost every home. We will get the radioactive atoms for one part of the lab from the air. None of the sources used in this lab are dangerous. Still, we will apply sensible rules that should always be applied to radioactive sources.

1. Minimize contact. Hold the needle sources by the stopper only. Keep them in their tubes when not in use. Hold the plastic disk sources by the edge. Don’t touch the actual source in the smoke detector. Decide what you are going to do with a source before you pick it up, and then do it.

2. Keep track. If your group is using one or more sources, each member should know where each source is. Never put the source in your pocket or hidden where it can’t be seen. Return the source to an AI when done.

3. No eating (or food) or drinking in the lab. Wash your hands when done.

4. When in doubt, ask an AI.

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Part I: Geiger-Mueller counter The Geiger-Mueller counter is a very sensitive device that can

detect the passage of individual particles (beta and gamma and maybe alpha rays) from radioactive decays. Because it can detect individual decays, it allows you to count them, hence “counter.” Your AI can describe how it works. Our G-M counters (GM-45s) are connected to computers, so the results can be stored and plotted. The computers are trained to make the traditional “clicks” that let you get a sense of how many decays are detected without plotting. We will find it most useful to measure the rate of detected decays. The computer does this by counting for a minute, plotting the result, then doing the same thing for the next minute, etc. The displayed rate is the counts per minute, or CPM.

• The instructors will demonstrate how to use the GM-45 counters. They will also introduce some of the concepts we need to study radioactivity.

Note that the counting is a statistical process (in this case, governed directly by quantum mechanics). Even with measurements of perfect precision, we do not expect to get the same number of counts in each minute! This means that we must do some averaging, either numerically or by eye. It also means that we must be patient and let the average unfold. During the longer measurements, you can work on Part II.

• First make sure the computer is operating and recording data. The first thing to measure is the room background, the rate of counts with no source present. This may be partly an occasional misfire of the GM-45, but it is mostly radioactivity in the materials used to make the device itself and in the air and other surroundings (including you). Record this number – you will want to subtract it from all measurements of other sources.

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• The AIs will give each group a source. Write down what your source is. Place it gently on the GM-45. Record the rate. Try some other sources.

• Use the ringstand and clamp to hold the Co-60 or Cs-137 source at various heights above the GM-45, say 4, 8, 16,… cm. Before you take the measurements, what do you expect to see? Plot the count rate vs. distance. Discuss the result.

• We can learn a bit about the radiation from the source by trying to block it. There are various sheets of materials from paper to metal in various thicknesses. Carefully remove the plastic cover from the smoke detector and the metal cover from the source itself, then put it face-down on the GM-45, as the AI did in the demo. Try the various materials between your source and the GM-45. Start with one, then 2, then more sheets of paper, then go to the heavier materials. What do you conclude about the source?

• Try this shielding test with another source if there is time. In a radioactive material, individual nuclei decay to other

nuclei, emitting particles that we call radiation (the old name was rays). We now know what these rays are: alpha rays are helium nuclei (these are made of two protons and two neutrons, an especially stable configuration that can be emitted as a unit from a larger, less stable nucleus); beta rays are electrons, and gamma rays are photons, the quantum-mechanical particles of light, but with energies much higher than visible light. X-rays are just less-energetic gamma rays.

If the radioactive nuclei are decaying, should they eventually be gone entirely? Yes! For the sources we’ve been using so far, this takes years (Co-60), or tens of years (Cs-137, Sr-90), or hundreds of years (Am-241), or even billions of years (K-40), so you haven’t seen it in your measurements.

When radioactive nuclei decay, they do so on an odd way. Each type of unstable nucleus has its own half-life: the time it

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takes for half of the individual nuclei of that type in a sample to decay. Example: the half-life of Americum-241 is 432 years. The odd thing is that after 432 years, when half the original Americium is gone, it is not the case that the other half is about to kick. In fact, half of the remainder will live another 432 years, exactly as if the whole surviving half had just been born. Your text calls this “dying, but not aging.”

The problem with doing experiments with radioactive nuclei with a half-life short enough to measure in a 3-hour lab is that if you buy some on Monday, it’s mostly gone by Tuesday. Instead, we need something that is made continuously that we can harvest and observe. Fortunately (in a sense, see below for the downside), uranium and thorium in the Earth’s crust is slowly decaying, and one of the resulting nuclei, Radon-222 (Rn-222), is a chemically inert but radioactive gas. It has a long enough half-life (about 4 days) that it can seep out of the ground. When it seeps into a basement, it can collect there, and, if levels are high, can become a health problem. The nuclei that Rn-222 decays to (see Figure 1) are metals. They stick to dust particles in the air, and we can collect and concentrate them onto a paper filter by using the yellow air samplers that have been running in the adjacent classroom. Note from the figure that lead-210 (210Pb) has a long half-life. It is thus a bottleneck, and what we will see is the decays that precede this. We will be most sensitive to the beta-decays of lead-214 and bismuth-214. Because we are seeing a chain of linked decays, we will not observe a single half-life. For example, for awhile, as long as there is 218Po (polonium-218), it will replenish the lead-214, and likewise, the decay of the lead-214 replenishes the bismuth-214. Still, the nuclei will decay in tens of minutes, and we can find when the decay rate drops to about half of its initial value.

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Figure 1. The radioactive decay sequence of uranium-238. The portions relevant to this lab are highlighted.

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• When you’ve read the above description, make another room background measurement by leaving your GM-45 with no source on it for a few minutes. Then place an unused paper filter on the GM-45 to see if it changes the count rate.

• Go with an AI to get a sample from the air samplers. Chose one and shut it off, noting the time and the time on the note indicating when the sampling started. Carefully remove the paper ring holding the filter paper and take the filter back and place it on your GM-45, noting the time again. (Note that holding the filter is no more dangerous than cleaning the filter in a clothes drier, which is doing the same thing that the air sampler did.)

You will leave this running for much of the rest of the lab. This would be a good time to do Part II.

• When you have enough data, use the graph made by the computer to estimate the half-life of this decay chain. (Call over the AI to help you print copies of the graph for your notebook.) Ignoring the fluctuations, approximately what shape should the graph be? Look back at Fig. 1 and think about whether your result for the half-life makes sense.

Part II: Cloud chamber – seeing the rays Set up: • In its operating state, the chamber should have isopropyl

alcohol soaked all the way up the blue filter paper on the side, with a couple mm of liquid on the bottom. If the whole thing is dry, add about 30 ml of isopropyl.

• Make sure there is ice in the water cooling bath (a beaker or Styrofoam cooler). Make sure the rubber hoses from the pump (small square black plastic thing) to the chamber and from the chamber to the bath are connected and the pump is

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submerged in the ice water. Plug in the pump and make sure the water is circulating.

• After the water has circulated for a few minutes, plug in the chamber. This does several things. It turns on a Peltier refrigerator in the base, cooling the bottom of the chamber. It applies a voltage to the yellow wire, which, if connected to the metal needle through the stopper, is intended to help clear away old tracks. It also turns on lights inside to illuminate the tracks.

If starting from scratch, it takes about 20 minutes for the chamber to show tracks.

How it works: The alcohol wicks up the sides of the chamber and evaporates

near the top, forming a clear vapor filling the chamber. The vapor near the bottom is cooled by the fridge in the base. In fact, it supercools, falling below the temperature at which it would normally be liquid. This state is unstable, needing only a triggering event to cause condensation. When ionizing radiation, that is, a charged particle such as a beta or alpha ray, passes through the vapor, it can remove electrons from the atoms, leaving a trail of positive ions along the path of the ray. The ions trigger the condensation of the supercooled alcohol vapor along the path of the ray, and the resulting tiny droplets form a visible track. Neutral particles such as gamma rays thus do not make tracks. However, a gamma ray can strike an electron in an alcohol molecule, transferring enough momentum to make the electron travel through the vapor. The electron (now identical to a beta ray) then leaves a track.

• When the chamber is working, you will start seeing little blobs of fog near the bottom. You may also see the occasional longer tracks. These are due to traces of radioactivity in the lab and also perhaps to cosmic rays, which are due to high energy radiation from space hitting the

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atmosphere. Watch them for awhile, noting where in the chamber the tracks form.

• Have the AI bring you a radioactive source. The “thoria” source produces alphas, the Sr-90 produces betas. These two needle sources can replace the stopper at the top of the chamber. Record notes on what you see in your notebook. Some sketches would be appropriate. The Co-60 and Cs-137 produce betas and gammas. These sources have to stay outside the chamber. Explore moving these sources around until you see the best tracks. Try blocking the radiation with the same materials used in Part I or other things lying around the lab. Again, record some notes on what you observe.