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jee

A heavy nucleus Q of half-life 20 minutes undergoes alpha-decay with probability of 60%  and beta-decay with probability...

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:
50
75
350
525
Solution:

Given,

T12=20 min

N0=1000

∵  1 hour=60 min=3T12

∴ Number of nuclei remain after 1 hour,

N=No23=10008

⇒N=125

It means 875 nuclei has decayed,

Now,

Number of α decayed Nucleus

=875×60100=525