38.17 - Radioactive decay and half-lives

Half-life: The time it takes for half of a group of

radioactive atoms to decay.

We have discussed the methods by which radioactive isotopes decay, by emitting Į,ȕ,

orȖ rays. What can be said about the rate at which they decay? If you have a sample of

radioactive atoms, how many of them will decay in, say, the next minute?

The answer depends on the radioactive isotope. For any isotope, the fraction of atoms

that will decay in a minute can be determined. A quantity of particular interest is the

half-life, which is the average time it takes for one-half of the radioactive material

present to decay.

For example, let’s consider 16.00 mg of a parent nuclide,^131 I, which is a radioactive

isotope of iodine. Its half-life is 8.04 days. You would find that after 8.04 days, one-half

of the parent nuclei have decayed, and 8.00 mg of^131 I remains. After another 8.04

days, one-half of the remaining iodine will have decayed, and 4.00 mg remains. After a

third 8.04 days, only 2.00 mg would remain, and after 8.04 more days, 1.00 mg would

remain, and so on. Half of the remaining iodine decays every 8.04 days.

If it is possible to know how many atoms in a sample are going to decay within a certain

time interval, is it possible to know when a particular atom will decay? Numerous

experiments have shown that the answer to that question for a particular atom is no.

This is similar to the situation of flipping one thousand coins and making a prediction of

“50% heads.” The prediction will be quite accurate, though you cannot reliably predict

the outcome of any particular coin. The process of radioactive decay provided evidence

of the statistical nature of quantum mechanics, which governs processes on a

subatomic scale.

Half-life

Average time for one-half of a group of

radioactive atoms to decay

During each half-life, one-half of

remaining radioactive atoms decay

Radioactive decay is

probabilistic

Cannot be predicted for an individual

atom

Can state the probability of any atom

decaying within a certain time

·or what fraction of the atoms will decay

within a certain time

38.18 - Interactive problem: radioactive dating

Carbon-14 is a radioactive isotope of carbon that has six protons and eight neutrons in its nucleus. It is commonly used to establish a date for

organic specimens. In the first simulation, you will observe the decay of carbon-14 (C-14), and determine the half-life of that radioactive

isotope.

You are equipped with a digital timer and a gauge that reports the number of parent atoms that are present. Before the simulation starts, there

are 32 billion parent atoms. Each of the spheres on the screen represents a billion atoms. A sphere changes color when a billion atoms have

decayed.

When you press GO, the timer starts and the carbon begins to decay to nitrogen by emitting ȕ rays, and the number of daughter nitrogen

atoms begins to grow. The daughter atoms are stable.

In the simulation, time is sped up and passes in thousands of years. The number of carbon atoms is shown both graphically with a

“thermometer”-type gauge as well as numerically. When half the initial number of parent atoms has become daughter atoms, press PAUSE

and note the elapsed time. (That is, at this moment, 16 billion of the carbon atoms remain present, and the rest have decayed.)

(^714) Copyright 2007 Kinetic Books Co. Chapter 38