HALF-LIFEChapter 7.2 – BC Science 10

Half - lifeThe time required for half ½ the nuclei in a

sample of a radioactive isotope to decayThe half life for any radioactive isotope is a

constant for any radioactive isotope.Each radioisotope decays at a unique rate

Time = 1 half life50% of sample (4 pennies) are still radioactive

Time = 2 half lives25% of sample (2 pennies) are still radioactive

Time = 3 half lives12.5% of sample (1 penny) still radioactive

Time = 4 half livesNo more pennies are radioactive.

Think about a sample with millions of atoms…

(c) McGraw Hill Ryerson 2007

7.2 Half-lifeIt can be difficult to determine the ages of

objects by sight alone.

Radioactivity provides a method to determine age.Measure the relative quantities of

remaining radioactive materialstable products formed.

See pages 302 - 304

(c) McGraw Hill Ryerson 2007

7.2 Half-lifeCarbon dating measures the ratio of carbon-12

and carbon-14.Stable carbon-12 and radioactive carbon-14 exist

naturally in a constant ratio.When an organism dies, carbon-14 stops being

created and slowly decays.Carbon dating only works for organisms less than 50

000 years old.

See pages 302 - 304

.

Carbon Dating – carbon-14

Living things replace the carbon-12 and carbon-14 in their bodies when they are alive.

However when living things die, they do not replace the carbon-14 as carbon-14 decays into nitrogen-14

Carbon-14 takes 5715 years to decay half of its nuclei into nitrogen-14

Carbon-12 remains unchanged.

Therefore something that has been alive within the past 50000 years contains enough nuclei of remaining carbon-14 to measure.

The ratio of carbon-12 and carbon-14 can estimate the age of the sample

Carbon Dating

Carbon datingThis picture shows a skeleton and a model for C-14 decay. The arrows

represent the amount of C-14 giving off it's radiation as time passes. Notice the amount goes down by half for every half life.

Decay CurveAll decay curves for any radioactive element

look the same except for the length of the half life.

(c) McGraw Hill Ryerson 2007

The Rate of Radioactive Decay

Half-life measures the rate of radioactive decay.

Half-life = time required for half of the radioactive sample to decay.

Strontium-90 has a half-life of 29 years. If you have 10 g of strontium-90 today, there will be 5.0 g remaining in 29 years.

See pages 305 - 306

The Rate of Radioactive Decay

Decay curves show the rate of decay for radioactive elements.

The curve shows the relationship between half-life and percentage of the original substance remaining.

The decay curve for strontium-90

(c) McGraw Hill Ryerson 2007

Common Isotope Pairs

Parent isotope = the original, radioactive material

Daughter isotope = the stable product of the radioactive decay

The rate of decay remains constant, but some elements require one step to decay while others decay over many steps before reaching a stable daughter isotope.

See page 307

(c) McGraw Hill Ryerson 2007

Common Isotope Pairs

There are many radioisotopes that can be used for dating.

Carbon-14 decays into nitrogen-14 in one step.Uranium-235 decays into lead-207 in 15 steps.Thorium-235 decays into lead-208 in 10 steps.

See page 307

Radioisotopes with very long half-lives can help determine the age of very old things.The potassium-40/argon-

40 clock has a half-life of 1.3 billion years.

Argon-40 produced by the decay of potassium-40 becomes trapped in rock.

Ratio of potassium-40 : argon-40 shows age of rock. See pages 307 - 308

The Potassium-40 Clock

See pages 307 - 308

The Potassium-40 Clock

K-40 Clock

Half-Life Practice Problems

1. If there are 50 grams of U-238 on day zero of radioactive decay, how much will there be after 4.5 billion years (1 Half Life)? A) 0.0 grams B) 10 grams C) 25 grams D) 50 grams

Solution to problem #1

Half-Life % Left Mass Time

0 100.000% 50

1 50.000% 25 4.5 BY2 25.000% 12.5

3 12.500% 6.25

4 6.250% 3.25

5 3.125%

Based on the graph, 2 half-lives equals A) 4.5 billion years. B) 9 billion years. C) 12.5 billion years. D) 18 billion years.

Solution to problem #1

Half-Life % Left Mass Time

0 100.000% 50

1 50.000% 25 4.5 BY

2 25.000% 12.5 9 BY

3 12.500% 6.25

4 6.250% 3.25

5 3.125%

Use the chart to determine the half-life of Carbon-14.

A) 5,000 years B) 5700 years C) 10,000 years D) 11,400 years

Practice Problems1. How long will it take 200

grams of Plutonium 239 (half life 24,400 years) to decay to 25 grams?

Practice Problems1. How long will it take 200

grams of Plutonium 239 (half life 24,400 years) to decay to 25 grams? Half-Life % Left Mass Time

0 100.000% 200 g 0 Years

1 50.000% 100 g 24,400 Y

2 25.000% 50 g 48,800 Y

3 12.500% 25 g 73200 Y

4 6.250%

5 3.125%

Practice Problems2. How many grams of iodine

131 (half life 8 days) would be left after 24 days if you start with 25 grams?

Practice Problems1. How many grams of iodine 131

(half life 8 days) would be left after 24 days if you start with 25 grams?Half-Life % Left Mass Time

0 100.000% 25 g 0 Days

1 50.000% 12.5 g 8 Days

2 25.000% 6.25 g 16 Days

3 12.500% 3.125 g 24 Days

4 6.250%

5 3.125%

A half-life is the length of time required for half the nuclei in a sample of a radioactive isotope to decay into its products.

Summary

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