Question

A particular nucleus in a large population of identical radioactive nuclei did survive 5 half lives of the isotope. Then the probability that this surviving nucleus will survive the next half life:

• A. 1/2
• B. 1/32
• C. 1/64
• D. It cannot be determined

Answer 1

Answer: (A)

The probability that this surviving nucleus will survive the next half-life is $\frac{1}{2}$ or 50%.

Answer 2

Radioactive decay is a memoryless process. This means the probability of a nucleus decaying in a given time interval is independent of how long the nucleus has already existed. The half-life ($T_{1/2}$) is the time interval during which any radioactive nucleus has a 50% probability of decaying and thus a 50% probability of surviving. The fact that the nucleus has survived 5 half-lives does not change the probability of it surviving the next half-life.