A counter recording radioactive decays from a radioactive source gives the following counts in equal intervals of time.

Question 20

A counter recording radioactive decays from a radioactive source gives the following counts in equal intervals of time.

time / min        counts

0–10                424

10–20              395

20–30              413

30–40              363

40–50              366

50–60              294

60–70              301

70–80              253

80–90              212

What can be deduced from these readings?

A that radioactivity is random and that the half-life is 90 minutes

B that radioactivity is random and that the half-life is uncertain

C that radioactivity is spontaneous and that the half-life is 90 minutes

D that radioactivity is spontaneous and that the half-life is uncertain

Reference: Past Exam Paper – November 2010 Paper 12 Q40

Solution:

Answer: B.

The half-life is uncertain because of the randomness of the decay – random counts are obtained in equal intervals of time.

Half-life is the time for the count to be halved.

Consider the values 424 (at time 0-10 min) and 212 (at time 80-90 min). If we are considering the lower limit for the count of 424 (that is, we are considering the 0 min instead of the 10 min), the same should be done for the count of 212.

Thus, half-life = 80 – 0 = 80 min.

Similarly, if we consider the upper limit.

Half-life = 90 – 10 = 80 min

So, the tine interval between the 424 and 212 readings is 80 min, not 90 min.