The half-life of a radioactive substance is `48` hours. How much time will it take to disintegrate to its `(1)/(16) th` parts ?

Options

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

Answer

D

Explanation

(d) `(N)/(N_0) = ((1)/(2))^(t//T) rArr (1)/(16) = ((1)/(2))^(t//48)`
`rArr ((1)/(2))^4 = ((1)/2)^(t//48) rArr t = 192 hours`.