P1bL8 Half Life
Key Words
Activity Rate - number of counts per second
Count rate - number of counts per second
Half life - the time taken for half the atoms in a sample to decay.
Isotope - a form of an element that contains the same number of protons but different number of neutrons to the normal element.
Radioactive decay - unstable nucleus changes into another element, giving out an alpha particle, beta particle, or gamma ray.
Radioisotope - an isotope of an element that is radioactive.
Grade E
Isotopes that have unstable nuclei and give out radiation are radioisotopes and they decay by radioactive decay, emitting alpha, beta, or gamma. The decay is random, and the rate of decay is taken as an average.
Nuclear physicists use the idea of half-life, which is defined as:
The time taken for half the original number of atoms to decay
The table below shows the way 10 000 atoms decay, when the half life is 10 hours.
| Time (h) | Number of atoms | Fraction left | Half-lives |
| 0 | 10 000 | 100 % | 0 (start) |
| 10 | 5000 | 50 % | 1 |
| 20 | 2500 | 25 % | 2 |
| 30 | 1250 | 12.5 % | 3 |
| 40 | 625 | 6.25 % | 4 |
| 50 | 313 | 3.125 % | 5 |
| 60 | 156 | 1.5625 % | 6 |
In other words, you start off with 1, then 1/2, then 1/4, 1/8, 1/16, and so on. In theory you never get to zero activity, but in practice, after about 6 - 7 half-lives, the activity is very low indeed.
Grade C
The half life of a radioisotope is a property of the element itself. You cannot increase the rate of decay by heating it, hitting it, squeezing it, pulling it to bits, or reacting it with reactive chemicals. Since the half-life is unique to that element, scientists use the half life to identify the element.
With a very big sample the rate of decay is even, but the smaller the sample, the more likely it is that the count rate will be uneven. So we have to use an average over a period of time.
Half lives vary from thousands of millions of years (uranium-238) down to a tiny fraction of a second (e.g. polonium-213).
Grade A
If we plot the activity of a radioactive decay against time, we get a graph that looks like this:
The shape of this graph is called an exponential decay.