isotope+half+life

Every radioisotope has a unique rate of decay. The standard way of reporting an isotope's decay rate is through half-life.

Half-life is defined as the amount of time in which exactly one half of a radioisotope has decayed into other products.

Examples:
 * uranium-238 has a half-life of 4.5 billion years. This means that of all the uranium-238 that existed at the creation of the Earth, about half has decayed into other elements.
 * radon-222 has a half-life of 3.8 days.
 * carbon-14 has a half-life of 5730 years, and is used by anthropologists to date organic matter.

Try [|this link] to help visualize radioactive decay.

Radioactive decay follows an exponential decay:

The half-life can be determined by dividing the y-axis maximum amount by two, and then obtaining the x value on the curve. The example above has a half-life of 2 days.

Another way of reporting the rate of radioactive decay is with a decay constant, //k//. This decay constant is a mathematical relationship to half-life:



Simply substitute a half-life value (example, 2 days) into the equation and solve for k:

2 days = 0.693/k

k = 0.693/2

k = 0.347 day^-1

The decay constant's units are "per time", or inverse time; just worry about the time unit (seconds, days, etc.) for our purposes.

Here is an Excel worksheet that you can use to experiment with half-life and decay curves.

The concept here is that after every half-life period, the amount of the original radioisotope is cut in half.

Suppose a 50.0 gram sample of a pure radioisotope of xenon-135 is made in a breeder reactor. This isotope has a half-life of 9 hours.

1. How long would it take for only 12.5 grams of xenon-135 to remain?
 * Determine how many half-lives have occurred by seeing how many times 50.0 g was cut in half.
 * 50.0 --> 25.0 --> 12.5
 * There have been two half-life periods, so 2 x 9 hours = 18 hours.
 * It takes 18 hours for xenon-135 to decay so that 12.5 grams remain.

2. How many grams of xenon-135 exist after 36 hours?
 * Determine how many half-lives have occurred: 36 divided by 9 is four half-life periods.
 * Cut the original mass, 50.0 grams, in half four times:
 * 50.0 --> 25.0 --> 12.5 --> 6.25 --> 3.125
 * Therefore, 3.125 grams of xenon-135 exist after 36 hours.

3. What is the decay constant for xenon-135?
 * The equation is set up as 9 hours = 0.693/k
 * k = 0.693/9
 * k = 0.077 per hour

Here is the course worksheet: