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:

Step-by-step solution

Given, T 1 2 = 20   min N 0 = 1000 ∵     1   hour = 60   min = 3 T 1 2 ∴ Number of nuclei remain after 1 hour, N = N o 2 3 = 1000 8 ⇒ N = 125 It means 875 nuclei has decayed, Now, Number of α decayed Nucleus = 875 × 60 100 = 525