1.1 What is Chemistry?

24.2. Half-Lives http://www.ck12.org

Answer:

Simply plug the given values into the equation above. Note that the units of the half-life and the total amount of time
must match.

Nt=N 0 ×( 0. 5 )

tt

1 / 2

Nt= ( 1. 8 × 104 c pm)×( 0. 5 )

1760. 67 minmin

Nt= ( 1. 8 × 104 c pm)×( 0. 5 )^3.^396

Nt= 1. 7 × 103 c pm

In this section, we have been looking at isotopes that decay directly to a stable nucleus. However, many isotopes,
particularly very heavy ones, require many successive decays before reaching a stable nucleus. For example,
the decay of uranium-238 results in the production of thorium-234, which is also radioactive. That decays into
protactinium-234, which is radioactive as well. The complete decay chain for uranium-238 is illustrated in the
Figure24.7.

Lesson Summary

• The half-life of an isotope is the amount of time necessary for one half of a given sample to undergo radioactive
  decay.


• Half-lives can vary from fractions of a second to millions of years.

Lesson Review Questions

Reviewing Concepts

1. Define half-life.


2. From the chart of half-lives referenced below, list the half-lives of:
   a. californium-251
   b. iodine-131
   c. uranium-238

Problems

1. An isotope has a half-life of 2.4 days. How many half-lives have passed if you measure the activity after 9.6
   days?


2. A radioactive sample has an initial activity of 36,000 cpm and a half-life of 14.6 minutes. What will be the
   activity after three half-lives?


3. A radioactive sample has an activity of 450 cpm three half-lives after the initial activity was determined. What
   was the original activity?


4. A sample of a certain isotope has an initial activity of 40,000 cpm. After 24.8 days, the activity is 2500 cpm.
   What is the half-life of this isotope?