Question

The count rate of a Geiger- Muller counter for the radiation of a radioactive material of half life of 30 minutes decreases to $5s^{-1}$ after 2 hours. The initial count rate was

• A. $25s^{-1}$
• B. $80s^{-1}$
• C. $625s^{-1}$
• D. $20s^{-1}$

Answer 1

The correct option is B $80s^{-1}$

$A=A_0{\left(\frac{1}{2}\right)}^{t/T_{1/2}}\Rightarrow 5=A_0{\left(\frac{1}{2}\right)}^{\frac{2\times 60}{30}}=\frac{A_0}{16}\Rightarrow A_0=80se{c}^{-1}$