A nucleus with Z =92 emits the following in a sequence:
`alpha,beta^(-),beta^(-),alpha,alpha,alpha,alpha,alpha,beta^(-),beta^(-),alpha,beta^(+),beta^(+),alpha`. The Z of the resulting nucleus is

Options

A. 76
B. 78
C. 82
D. 74

Answer

D

Explanation

Given, `T_(1//2)=20" min",N_(1)=50`
`N_(2)=100-87.5=12.5`
We know that, time taken by a substance to decay,
`t_(2)-t_(1)=(T)/(ln2)ln((N_(1))/(N_(2)))=(20)/(ln2)ln[(50)/(12.5)]=(20)/(ln2)ln4=40`min