5 Steps to a 5 AP Chemistry

Nuclear Chemistry  263

enough neutrons (or has too many protons) to be stable. Decay modes which increase the

number of neutrons, decrease the number of protons, or both, would be favored. Both

positron emission and electron capture accomplish this by converting a proton into a

neutron. As a general rule, positron emission occurs with lighter isotopes and electron

capture with heavier isotopes.

Isotopes that are neutron-rich, that have too many neutrons or not enough protons, lie

above the belt of stability and tend to undergo beta emission because that decay mode con-

verts a neutron into a proton.

A particular isotope may undergo a series of nuclear decays until finally a stable isotope

is formed. For example, radioactive U-238 decays to stable Pb-206 in 14 steps, a majority

of which are alpha emissions, as one might predict.

Nuclear Decay Calculations

A radioactive isotope may be unstable, but it is impossible to predict when a certain atom

will decay. However, if a statistically large enough sample is examined, some trends

become obvious. The radioactive decay follows first-order kinetics (see Chapter 14 for

a more in-depth discussion of first-order reactions and equations). If the number of

radioactive atoms in a sample is monitored, it can be determined that it takes a certain

amount of time for half the sample to decay; it takes the same amount of time for half the

remaining sample to decay; and so on. The amount of time it takes for half the sample to

decay is called the half-life of the isotope and is given the symbol t1/2. The table below

shows the percentage of radioactive isotope remaining versus half-life.

HALF-LIFE,t1/2 PERCENT RADIOACTIVE ISOTOPE REMAINING

0 100

150

225

3 12.5

4 6.25

5 3.12

6 1.56

7 0.78

8 0.39

9 0.19

10 0.09

As a general rule, the amount of radioactivity at the end of 10 half-lives drops below

the level of detection and the sample is said to be “safe.”

Half-lives may be very short, 4.2 × 10 −^6 seconds for Po-213, or very long, 4.5 × 109

years for U-238. The long half-lives of some waste products is a major problem with nuclear

fission reactors. Remember, it takes 10 half-lives for the sample to be safe.

If only multiples of half-lives are considered, the calculations are very straightforward.

For example, I-131 is used in the treatment of thyroid cancer and has a t1/2of eight days.

How long would it take to decay to 25% of its original amount? Looking at the chart, you

see that 25% decay would occur at two half-lives or 16 days. However, since radioactive