Modern Physics 3 Question 40

39. At a given instant there are 25 undecayed radioactive nuclei in a sample. After 10s the number of undecayed nuclei reduces to 12.5. Calculate

(1996,3 M)

(a) mean life of the nuclei,

(b) the time in which the number of undecayed nuclei will further reduce to 6.25 of the reduced number.

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Solution:

  1. (a) In 10s, number of nuclei has been reduced to half (25% to 12.5.

Therefore, its half-life is t1/2=10s

Relation between half-life and mean life is

tmean =t1/2ln(2)=100.693stmean =14.43s

(b) From initial 100 to reduction till 6.25, it takes four half lives.

100t=4t1/2=4(10)s=40st=40s



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