A parent nucleus X is decaying into daughter nucleus Y which in turn decays to Z. The half lives of X and Y are 40000 years and 20 years respectively. In a certain sample, it is found that the number of Y nuclei hardly changes with time. If the number of X nuclei in the sample is `4 xx 10^(20)`, the number of Y nuclei present in its is–

Options

A. `2 xx 10^(17)`
B. `2 xx 10^(20)`
C. `4 xx 10^(23)`
D. `4 xx 10^(20)`

Answer

a

Explanation

`X overset(.^(lambda)X)(to) Y overset(.^(lambda)gamma)(to) Z`
At equlibrium
`lambda_(x) N_(X) = lambda_(gamma N_(gamma)`
`N_(gamma) = (lambda_(X))/(lambda_(Y)) xx N_(X)` `:' t_(1//2) = (0.693)/(lambda)`
`((t_(1//2))_(gamma))/((t_(1//2))_(X)) xx N_(X)`
`= (20)/(40000) xx 4 xx 10^(20) = 2 xx 10^(17)`