Question

A freshly prepared radioactive source of half-life 2h emits radiation of intensity which is 64 times the permissible safe level. Calculate, the minimum time after which it would be possible to work safely with this source.

• A. 12 h
• B. 24 h
• C. 6 h
• D. 130 h

Answer 1

Answer: (A)

12 h

The intensity of radioactive decay after time $t$ is $I\left(t\right)=I_0{e}^{-kt}$

Hence half life is given by $\tau =\frac{ln2}{k}=2h$

$⟹k=\frac{ln2}{2}{h}^{-1}$

The intensity must drop to $1/64$ of its present intensity to work safely.

Hence, $\frac{I_0}{64}=I_0{e}^{-t\left(ln2\right)/2)}$

$⟹\frac{tln2}{2}{h}^{-1}=ln64$

$⟹t=12h$