Question

The counting rate observed from a radioactive source at t=0 second was 1600 counts per second and at t=8 seconds it was 100 counts per second. The counting rate observed as counts per second at t=6 seconds, will be

• A. $200$
• B. $400$
• C. $300$
• D. None of these

Answer 1

The correct option is A $200$

$\begin{array}{c}A=A_0{\left(\frac{1}{2}\right)}^{\frac{t}{T_1/2}}\\ 100=1600{\left(\frac{1}{2}\right)}^{\frac{t}{T_1/2}}\\ T_1/2=2\sec \\ againatt=6\sec \\ A=1600{\left(\frac{1}{2}\right)}^{\frac{6}{2}}=200counts/\sec \end{array}$

Hence,

option $\left(A\right)$ is correct answer.