Half-life
When unstable atoms give off particles that can be harmful to humans. decay is a Occurring without a pattern. Unpredictable. In statistics where each item has an equal probability of being selected. process. Even if a The central part of an atom. It contains protons and neutrons, and has most of the mass of the atom. The plural of nucleus is nuclei. 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 The smallest part of an element that can exist.. Some of its unstable Nuclei is the plural of nucleus. The nucleus is the central part of an atom. It contains protons and neutrons, and has most of the mass of the atom. 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 The time it takes for the number of nuclei of a radioactive isotope in a sample to halve. Also defined as the time it takes for the count rate from a sample containing a radioactive isotope to fall to half its starting level. of a radioactive Atoms of an element with the same number of protons and electrons but different numbers of neutrons. 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 Measure of the amount of radiation reaching a detector in a given time, usually shown as counts per second or counts per minute. measured by a detector such as a Device used to detect and measure the quantity of ionising radiation in an area.. 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 |
| Time (days) | 0 |
|---|---|
| Total number of half-lives | 0 |
| Count rate (counts/s) | 8,000 |
| Time (days) | 4 |
|---|---|
| Total number of half-lives | 1 |
| Count rate (counts/s) | 4,000 |
| Time (days) | 8 |
|---|---|
| Total number of half-lives | 2 |
| Count rate (counts/s) | 2,000 |
| Time (days) | 12 |
|---|---|
| Total number of half-lives | 3 |
| Count rate (counts/s) | 1,000 |
| Time (days) | 16 |
|---|---|
| Total number of half-lives | 4 |
| Count rate (counts/s) | 500 |
| Time (days) | 20 |
|---|---|
| Total number of half-lives | 5 |
| Count rate (counts/s) | 250 |
| Time (days) | 24 |
|---|---|
| Total number of half-lives | 6 |
| Count rate (counts/s) | 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: \(\frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2}\))