Radioactive decay & datingHomework 02

Read through the information below, then for each of the 10 questions write the letter (A, B, C or D) and copy the correct statement into your exercise book.

Alpha decayUranium is radioactive, because it undergoes alpha decay … it emits an alpha particle from its nucleus to make itself more stable. parent atom daughter atom

23892U 234

90Th + 42α

This is a nuclear equation, and it shows that alpha decay of uranium produces an alpha particle, and also a new element called thorium (‘Th’). Notice that the nuclear equation balances (just like a chemical equation).

Alpha decay always produces a new element, whichis found 2 spaces to the left in the periodic table

Radon gas also decays in this way, this time to produce polonium. Notice that we can also represent the alpha particle as a helium nucleus … parent atom daughter atom

22286Rn 218

84Po + 42He

Beta decayThorium undergoes beta decay … it emits a beta particle from its nucleus and changes into an atom of protactinium . The following nuclear equation also balances … parent atom daughter atom

23490Th 234

91Pa + 0-1β

Beta decay always produces a new element, whichis found 1 space to the right in the periodic table

Lead also decays in this way, this time to produce bismuth. Notice that we can also represent the beta particle as an electron … parent atom daughter atom

21482Pb 214

83Bi + 0-1e

Gamma decaySometimes, alpha decay and beta decay produce a nucleus in an ‘excited state’. This is a nucleus that has too much energy. This energy is lost by emitting a burst of gamma radiation.

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Half-life A Geiger counter will measure the count rate from a radioactive source, and this enables us to plot a line graph of ‘count rate’ against ‘time’. The graph has a characteristic shape, from which we can take measurements of the half-life of the substance …

Half-life = time it takes for ½ of the radioactive substance to decay

After 2 half-lives have occurred, only ¼ of the substance will remain!

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Time (seconds)

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Radioactive decay-curve showing half-life

1st half-life 2nd half-life 3rd half-life

It is important to notice that over the 1st half-life of 4 seconds the percentage of undecayed nuclei falls by ½ (100 50)

Over the next half-life the percentage of undecayed nuclei falls by ½ again (50 25) and the length of this half-life is the same as the previously half-life; 4 seconds

Over the third half-life the percentage of undecayed nuclei falls by ½ yet again(25 12½), this also takes 4 seconds

All the half-lives of this particular isotope will last 4 seconds

Dating the Earth

When U-238 decays, it produces a series of different elements that eventually result in the stable isotope, Pb-206…

solid arrows = alpha decays dotted arrows = beta decays

We know that virtually all of the lead on our planet used to be a radioisotope of uranium

Today, there is roughly the same amount of U-238 and Pb-206 on our planet

By far the longest half-life in the series of decays is the half-life for U-238 to form Th-234 … (the first step) … 4.5 billion years

Our Earth must have been through one ½ life of U-238, if half of the original amount of uranium has decayed

The Earth is roughly 4.5 billion years old.

Dating igneous rocks

Igneous rock often contains a radioisotope of potassium (K-40), which undergoes beta decay to form gaseous argon (Ar-40). We know thatK-40 has a half-life of 1.3 109 years, and so if we can find the relative amounts of K-40 and Ar-40 in a rock, we can say how old it is.

eg. If a rock contains equal amounts of K-40 and Ar-40, then half of the potassium must have decayed, and the rock must be 1.3 109

years old.

Carbon dating

Carbon dioxide molecules in the air mainly contain carbon-12, but some contain the radioisotope, carbon-14. The proportion of C-14 has stayed the same, because it is made (when cosmic rays bombard nitrogen-14) at the same rate at which it decays. Both of these isotopes become part of plants and animals, as a result of photosynthesis … the C-14 then decays inside the plant or animal (but no C-14 is formed inside them).

We can find the age of material that was once living by comparing the amounts of C-12 and C-14 within it, with the amounts of C-12 and C-14 in the atmosphere. (The half-life of C-14 is 5 730 years).

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23892 U

23490 Th

23491 Pa

23492 U

23090 Th

22688 Ra

22286 Rn

21884 Po

21482 Pb

21483 Bi

21484 Po

21082 Pb

21083 Bi

21084 Po

20682 Pb

Q1 A – Alpha decay of uranium produces an alpha particle, and also a new element called thorium … 238

92U 23289Th + 4

2α B – Radon gas also decays by alpha emission, to produce polonium … 222

86Rn 21684Po + 3

2H C – Alpha decay of uranium produces an alpha particle, and also a new element called thorium … 238

92U 23491Th + 4

1α Radon gas also decays by alpha emission, this time to produce polonium 222

86Rn 22287Po + 0

-1β D – Alpha decay of uranium produces an alpha particle, and also a new element called thorium … 238

92U 23490Th + 4

2α Radon gas also decays in this way, this time to produce polonium … 222

86Rn 21884Po + 4

2He

Q2 A – Beta decay always produces a new element, which is found 2 spaces to the left in the periodic table. A parent atom decays to form a daughter atom B – Alpha decay always produces a new element, which is found 2 spaces to the left in the periodic table. A daughter atom decays to form a parent atom C – Alpha decay always produces a new element, which is found 2 spaces to the left in the periodic table. A parent atom decays to form a daughter atom D – Alpha decay always produces a new element, which is found 1 space to the left in the periodic table. A parent atom decays to form a daughter atom

Q3 A – Thorium undergoes beta decay when it emits a beta particle from its nucleus 234

90Th 23391Pa + 0

-1β Lead also decays in this way, this time to produce bismuth 214

82Pb 21483Bi + 1

-1e B – Thorium undergoes beta decay when it emits a beta particle from its nucleus 234

90Th 23491Pa + 0

-1β Lead also decays in this way, this time to produce bismuth 214

82Pb 21483Bi + 0

-1e C – Thorium undergoes beta decay when it emits a beta particle from its nucleus 234

90Th 23591Pa + 0

-1α D – Lead decays by beta emission, to produce bismuth 214

82Pb 21683Bi + 0

-1e

Q4 A – Beta decay always produces a new element, which is found 2 spaces to the right in the periodic table B – Beta decay always produces a new element, which is found 1 space to the right in the periodic table C – Beta decay always produces a new element, which is found 1 space to the left in the periodic table D – Beta decay always produces a new element, which is found 2 spaces to the left in the periodic table

Q5 A – Sometimes, alpha decay and beta decay produce a nucleus in an ‘excited state’, which needs to lose energy by emitting infrared radiation B – Sometimes, alpha decay and gamma decay produce a nucleus in an ‘excited state’, which needs to lose energy by emitting beta radiation C – Sometimes, alpha decay and beta decay produce electrons in an ‘excited state’. These need to lose energy by emitting gamma radiation D – Sometimes, alpha decay and beta decay produce a nucleus in an ‘excited state’, which needs to lose energy by emitting a burst of gamma radiation

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Q6 A – A Geiger counter will estimate the count rate from a radioactive source, and this enables us to plot a line graph of ‘count rate’ against ‘time’ B – A Geiger counter will measure the count rate from a radioactive source, and this enables us to plot a line graph of ‘count rate’ against ‘time’. The half-life of a substance is the time it takes for ½ of it to decay C – The half-life of a substance is half the time it takes for it to decay D – The half-life of a substance is a quarter of the time it takes for it to decay

Q7 A – Virtually all of the lead on our planet used to be a radioisotope of uranium. Today, there is roughly the same amount of U-238 and Pb-206 on our planet B – Virtually all of the uranium on our planet used to be a radioisotope of lead C – Today, there is roughly half the amount of U-238, as there is Pb-206 on our planet D – Today, there is roughly twice the amount of U-238, as there is Pb-206 on our planet

Q8 A – Our Earth must have been through two ½ lives of U-238, if half of the original amount of uranium has decayed B – Our Earth must have been through ½ a life of U-238, if half of the original amount of uranium has decayed C – Our Earth must have been through one ½ life of U-238, if half of the original amount of uranium has decayed. This means that the Earth is roughly 4.5 million years old D – Our Earth must have been through one ½ life of U-238, if half of the original amount of uranium has decayed. This means that the Earth is roughly 4.5 billion years old

Q9 A – Igneous rock often contains a radioisotope of potassium (P-40), which Undergoes beta decay to form gaseous argon (Ar-40) B – Igneous rock often contains a radioisotope of potassium (K-40), which Undergoes beta decay to form gaseous argon (Ar-40). If we can find the relative amounts of K-40 and Ar-40 in a rock, we can say how old it is C – Igneous rock often contains a radioisotope of potassium (K-40), which undergoes alpha decay to form gaseous argon (Ar-40). If we can find the relative amounts of K-40 and Ar-40 in a rock, we can say how old it is D – Igneous rock often contains a radioisotope of potassium (K-40), which undergoes alpha decay to form gaseous neon (Ne-40)

Q10 A – We can find the age of animals by comparing the amounts of C-12 and C-14 they contain, with the amounts of C-12 and C-14 in the atmosphere B – We can find the age of material which was once living by comparing the amounts of C-12 and C-13 it contains, with the amounts of C-12 and

C-13 in the atmosphere. (The ½ life of C-14 is 5 730 years) C – We can find the age of material which was once living by comparing the amounts of C-12 and C-14 it contains, with the amounts of C-12 and C-14 in the atmosphere. (The ½ life of C-14 is 5 730 years) D – We can find the age of material which was once living by comparing the amounts of C-12 and C-14 it contains, with the amounts of C-12 and

C-14 in the atmosphere. (The ½ life of C-14 is 5 370 years)

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