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Q.

A heavy nucleus Q of half life 20 minutes undergoes alpha-decay with a probability of 60% and beta-decay with a probability of 40%. Initially, the number of Q nuclei is 1000. The number of alpha-decays of Q in the first one hour is m × 10 . Find ‘m’.

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answer is 52.5.

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Detailed Solution

t1/2=20min
In 60min, no.of half-life = 3
=1000-1000(1/2)3 = 875
The number of alpha-decays of Q in the first one hour  =875×0.6=525

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