Question: 2. A freshly prepared radioactive source of half life 2 hrs emits radiation of intensity which is 32 times the permissible safe value of intensity. Which of the following is the minimum time after which it would be possible to work safely with this source ?
(A) 16 hrs
(B) 5 hrs
(C) 10 hrs
(D) 32 hrs
(A) 16 hrs
(B) 5 hrs
(C) 10 hrs
(D) 32 hrs
Answers & Comments
Verified answer
Answer:
The intensity of radioactive decay after time t is I(t)=[tex]=Io\ e^{-kt}[/tex]
Hence half life is given by [tex]τ =\frac{ln2}{k} =2h[/tex]
⟹k=[tex]\frac{ln2}{2} h^{-1}[/tex]
The intensity must drop to 1/64 of its present intensity to work safely.
Hence, [tex]\frac{Io}{32} =Io \ e^{-t ln2/2}[/tex]
therefore ⟹t=6h
hence option (c) is correct