A heavy nucleus Q of half-life 20 minutes undergoes alpha-decay with probability of 60% and beta-decay with probability of 40%. Initially, the number of Q nuclei is 1000. The number of alpha-decays of Q in the first one hour is

(A) 50        (B) 75        (C) 350        (D) 525

Solution

If $N_0$ be the initial number of nuclei and N the number after n half-lives, then

$\frac {N}{N_0}=(\frac {1}{2})^n$

Here, $\frac {N}{1000}=(\frac {1}{2})^3$

$\therefore N = 125$

Total number of decays = 1000 – 125 = 875

Total number of alpha-decays = 60% of 875 = 525

Hence, Option (D).