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…

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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:

MARKS Content Team · Accepted Answer

Correct answer: (D) 525. Given, T_12=20 min N_0=1000 ∵ 1 hour=60 min=3T_12 ∴ Number of nuclei remain after 1 hour, N=N_o2^3=1000/8 ⇒N=125 It means 875 nuclei has decayed, Now, Number of α decayed Nucleus =(875×60)/100=525

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:

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