Question

The count rate of a radioactive source at t=0 was 1600counts/s and at t=8s, it was 100counts/s. The count rate (in counts) at t = 6s will be

• A. 150
• B. 200
• C. 300
• D. 400

Answer 1

The correct option is B 200

At $t=0,$ $1600counts/s$

At $t=8s,$ $100counts/s$

$K=\frac{0.693}{8}ln\left(16\right)$

So, count at $t=6sec,$

$\frac{0.693}{8}ln\left(16\right)=\frac{0.693}{6}ln\left(\frac{1600}{counts}\right)$

$\Rightarrow \frac{3}{4}ln\left(16\right)=ln\left(\frac{1600}{counts}\right)$

$\Rightarrow counts=\frac{1600}{8}=200$