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.

Y axis shows amount the percentage of carbon 14 remaining (0-100).  X axis shows time in years beginning at 0 and ending at 28500.  The curve goes from 100 on the y axis down to 28500 on the x axis.A graph showing how the amount of carbon-14 atoms in a sample would change over time

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-livesCount rate (counts/s)
008,000
414,000
822,000
1231,000
164500
205250
246125

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})