Question

Using a nuclear counter the count rate of emitted particles from a radioactive source is measured. At $t=0$ it was $1600$ counts per second and $t=8$ seconds it was $100$ counts per second. The count rate observed, as counts per second, at $t=6$ seconds is close to

• A. $150$
• B. $360$
• C. $200$
• D. $400$

Answer 1

Answer: (C)

$200$

At $t=0,A_0=\frac{dN}{dt}=1600C/s$
at $t=8s,A=100C/s$
$\frac{A}{A_0}=\frac{1}{16}$ in $8sec$
Therefore half life is $t_{1/2}=2sec$
$\therefore$ Activity at $t=6$ will be $1600{\left(\frac{1}{2}\right)}^3$
$=200C/s$
$\therefore$ correct answer is $\left(3\right)$.