1.1 What is Chemistry?

http://www.ck12.org Chapter 24. Nuclear Chemistry

FIGURE 24.6

This graph shows a decay curve in terms

of half-lives and mole percent of the sub-

stance remaining. This is an example of

exponential decay.

case, the measured activity will decrease to one-half of its original value after one half-life has passed. For example,
if one hour is required for the radioactivity of a certain sample to decrease from 30,000 cpm to 15,000 cpm, that
isotope has a half-life of one hour.

Example 24.1

The isotope iodine-125, which is used in certain medical procedures, has a half-life of 59.4 days. How many half-
lives have passed after 178.2 days? If the initial activity of a sample of iodine-125 is 32,000 cpm, what will be its
activity after 178.2 days?

Answer:

Since we know that one half-life is equal to 59.4 days, we can determine the number of half-lives as follows:

178 .2 days×1 half 59 .4 days−life=3 half−lives

Because this value is a whole number, we can simply divide the original activity in half once for each half-life:

initial activity = 32,000 cpm

after one half-life = 16,000 cpm

after two half-lives = 8,000 cpm

after three half-lives = 4,000 cpm

If the amount of time that has passed is not a simple multiple of the known half-life, we can use the following
equation:

Nt=N 0 ×( 0. 5 )

tt

1 / 2

where Ntis the amount of activity at time t, N 0 is the initial activity (at time = 0), t is the amount of time that has
passed, and t 1 / 2 is the half-life of the isotope.

Example 24.2

Rubidium-78 has a half-life of 17.67 minutes. If a given sample of Rb-78 has a measured activity of 1.8× 104 cpm,
what will be its activity after one hour has passed?