Half-life, Contamination & Irradiation

Half-life

• Radioactive decay is random, but with a large number of nuclei the overall rate is predictable
• The half-life of a radioactive isotope is the time it takes for the number of nuclei in a sample to halve, or the time for the count rate (or activity) to fall to half its initial level
• After one half-life half the original nuclei remain; after two, a quarter; after three, an eighth. The activity halves the same way
• Finding a half-life from a graph: read the time for the activity to fall from any value to half of it. Check with a second pair of values
• Worked example: a source's count rate falls from 800 to 100 counts per second in 24 hours. $800 \rightarrow 400 \rightarrow 200 \rightarrow 100$ is three half-lives, so the half-life is 8 hours
• (HT) Net decline as a ratio: after $n$ half-lives the activity is $\left(\tfrac{1}{2}\right)^n$ of the original. After 3 half-lives it is $\frac{1}{8}$, so the ratio of remaining to original is 1 : 8, and the fraction that has decayed is $\frac{7}{8}$
• Activity from a decay curve: the activity at a time is the gradient of the tangent to the graph of number of nuclei against time, in Bq