A radioactive substance has a half life of `60` minutes. After `3` hours, the fraction of atom that have decayed would be.

Options

A. `12.5 %`
B. `87.5 %`
C. `8.5 %`
D. `25.1 %`

Answer

B

Explanation

(b) `N = N_0 ((1)/(2))^((t)/(T_1 //2))`
Hence, fraction of atoms decayed
=`1 - (N)/(N_0) = 1 - ((1)/(2))^((t)/(T_1//2)) = 1 - ((1)/2)^((3 xx 60)/(60)) = (7)/(8)`
In percentage it is `(7)/(8) xx 100 = 86.5 %`.