Radioactive emissions
Unstable atomic nuclei emit radiation. Each type of radiation has different properties and interacts with matter in varying ways. Radioactive decay is random but can be measured. People are exposed to sources of radiation in all aspects of everyday life. Radioactive sources can be very useful but need handling carefully to ensure safety.
Half-life
Radioactive decay is a random process. Even if a nucleus is unstable, there is no way to tell whether it will decay in the next instant, or in millions of years’ time.
However, even tiny pieces of material contain very many atoms. Some of its unstable nuclei decay in a short time, while others decay much later. So, we use the time in which half of any of these unstable nuclei will decay.
The half-life of a radioactive isotope is the time taken for half the unstable nuclei in a sample to decay.
Different isotopes have different half-lives. Plutonium-239 has a half-life of 24,100 years but plutonium-241 has a half-life of only 14.4 years.
The half-life of a particular isotope is unaffected by chemical reactions or physical changes. For example, radioactive decay does not slow down if a radioactive substance is put in a fridge.
Using half-life
Half-life can be used to work out the age of fossils or wooden objects. Living things absorb carbon dioxide and other carbon compounds. Some of the carbon atoms are carbon-14, which is a radioactive isotope of carbon. Carbon-14 has a half-life of about 5,700 years.
When a living thing dies, it stops absorbing carbon-14. This means the amount of carbon-14 will decrease over time. The amount left can be compared to currently living organisms and an approximate age given for the fossil. For example, if an ancient dead tree contains half the expected amount of carbon-14, it must have died about 5,700 years ago.
Calculating net decline - Higher
Radioactive decay causes a reduction in the number of unstable nuclei in a sample. In turn, this reduces the count rate measured by a detector such as a Geiger-Muller tube. Another way to define the half-life of a radioactive isotope is the time taken for count rate from a sample to decrease by a half.
The table shows how the count rate of an isotope might change over time.
| Time (days) | Total number of half-lives | Count rate (counts/s) |
|---|---|---|
| 0 | 0 | 8,000 |
| 4 | 1 | 4,000 |
| 8 | 2 | 2,000 |
| 12 | 3 | 1,000 |
| 16 | 4 | 500 |
| 20 | 5 | 250 |
| 24 | 6 | 125 |
Notice how the count rate falls to half its previous value every four days. This is the half-life of the isotope.
The net decline in radioactive emissions after 3 half-lives = 1,000/8,000
= 1/8th
(Note that this is equal to: \(\frac{1}{2} \times \frac{1}{2} \times \frac{1}{2}\))
- Question
Use the table to determine the net decline, expressed as a ratio, after 6 half-lives.
count rate at start = 8,000 count/s
count rate after 6 half-lives = 125 counts/s
net decline = 125/8,000
= 1/64th
(Note that this is equal to: \(\frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2}\))