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).