Question

The half-life of a radioactive substance is 48 hours. How much time will it take to disintegrate to its $\frac{1}{16}$th part.

• A. 12 h
• B. 16 h
• C. 48 h
• D. 192 h

Answer 1

Answer: (D)

192 h

Answer 2

$\frac{N}{N_{0}} = \left( \frac{1}{2} \right)^{t/T} \Rightarrow \frac{1}{16} = \left( \frac{1}{2} \right)^{t/48}$

$\Rightarrow \left( \frac{1}{2} \right)^{4} = \left( \frac{1}{2} \right)^{t/48} \Rightarrow t = 192\mspace{6mu} hour.$