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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-decays of Q in the first one hour is:

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a

50

b

75

c

350

d

525

answer is D.

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Detailed Solution

Total number of decays in one hour are given as
 Nd=[1−(12)t/T]×N0
 ⇒Nd=[1−(12)3]×1000=78×1000=875
Thus number of  α−decays are given as
Nd=875×60%=525 

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