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Lesson: Radioactive Decay Physics

In this lesson, we will learn how to calculate the change in the activity of a radioactive sample after a given amount of time has passed.

Lesson Plan

Students will be able to

use in all permutations to relate , the half-life of a radioactive isotope, to , the mean lifetime of a nucleus of that isotope,
use in all permutations to relate , the half-life of a radioactive isotope, to , the decay constant of that isotope,
use in all permutations to relate , the mean lifetime of a nucleus of an isotope, to , the decay constant of that isotope,
use in all permutations, where is the number of atoms of a given radioactive isotope at time , is the initial number of atoms, and is the half-life of the isotope,
use in all permutations,
use in all permutations, where is the activity of a given radioactive sample at time , is the initial activity, and is the half-life,
use in all permutations.

Lesson Worksheet

Q1:

A radioactive isotope has a half-life of 1,380 years. What proportion of a sample of the isotope would remain after 4,000 years? Give your answer to three decimal places.

Q2:

A sample of pure cobalt-57 is left in a sealed container for 100 days. At the end of the 100 days, the cobalt is taken out of the container. Its activity is measured and found to be 540 Bq. Cobalt-57 has a half-life of 272 days. What was the activity of the sample at the start of the 100 days? Give your answer to the nearest becquerel.

Q3:

Carbon-11 has a half-life of 20.3 minutes. The activity of a sample of pure carbon-11 is found to be 7,200 Bq. What will the activity of the sample be 4 hours later? Give your answer to two decimal places.