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-decay of Q in the first one hour is

Question

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-decay of Q in the first one hour is (A) 50 (B) 75 (C) 350 (D) 525

Tardigrade Admin · Accepted Answer

Total no. of decays in 60 minutes =1000-1000((1/2))3=875 So, no. of α-decay =875 × 0.6=525

Q. 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-decay of $Q$ in the first one hour is

50

75

350

525

Total no. of decays in $60$ minutes
$= 1000 - 1000 (\frac{1}{2})^{3} = 875$
So, no. of $α$ -decay $= 875 \times 0.6 = 525$

Q. 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-decay of Q in the first one hour is

50

75

350

525

Total no. of decays in 60 minutes =1000−1000(21​)3=875 So, no. of α-decay =875×0.6=525

Q. 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-decay of $Q$ in the first one hour is

Total no. of decays in $60$ minutes
$= 1000 - 1000 (\frac{1}{2})^{3} = 875$
So, no. of $α$ -decay $= 875 \times 0.6 = 525$