Question

The activity of a radioactive sample is measured as $9750$ counts per minute at $t=0$ and as $975$ counts per minute at $t=5$ minutes. The decay constant is approximately,

• A. $0.922$ per minute.
• B. $0.691$ per minute.
• C. $0.461$ per minute.
• D. $0.230$ per minute.

Answer 1

Answer: (C)

According to radioactivity decay law, the number of decays per second is directly proportional to the number of active samples.
$\frac{d N}{d t}=\lambda N$
$9750=\lambda N_{0}$ .... (i)
$975 = \lambda N$ .... (ii)
Dividing (i) by (ii),
$\frac{N}{N_{0}} = \frac{1}{10}$ .
We know that,
$\lambda =\frac{2.303}{t}log\frac{N_{0}}{N}$
$=\frac{2 .303}{5}log10$
$= 0.4606 = 0.461$ per minute.