Question

For a radioactive sample, the initial activity of the material was $8$ $cps$ and after $3 \, h$ it becomes $1$ $cps$ . The half-life of the sample is

• A. $2h$
• B. $1 \, h$
• C. $3h$
• D. $4h$

Answer 1

Answer: (B)

Here $A_{0} \, = \, 8$ counts, $A=$ $1$ count and $t=3 \, h$ .
$\frac{A}{A_{0}}=\left(\frac{1}{2}\right)^{n}$
$⇒ \, \frac{1}{8}=\left(\frac{1}{2}\right)^{n}$
or $\left(\frac{1}{2}\right)^{3}=\left(\frac{1}{2}\right)^{n}\Rightarrow n=3$
So, $T_{1 / 2} \, = \, \frac{t}{n} \, = \, \frac{3}{3}= \, 1 \, h$