Radioactive decay follows first order kinetics and the rate constant is often termed as decay constant. Certain radioactive substances may undero sequential decays in order to convert into a stable nucleus. The series comprising all such elements is termed as radioactive disintegration series.
A substance A undergoes sequential decay as shown `A overset(lambda_(1))rarr B overset (lambda_(2))rarr C`. If the decay constant `lambda_(1)` and `lambda_(2)` are `4 xx10^(-2) "min"^(-1)` and `16 xx 10^(5) "min" ^(-1)` respectively then the molar ratio of B to A after a very long time will be :

Options

A. `2.5 xx 10^(-8)`
B. `4 xx 10^(-2)`
C. `(1)/(16 )xx 10^(-5)`
D. `4 xx 10^(7)`

Answer

A

Explanation

`[._(z)X^(A) underset (-alpha)rarr ._(z-2)X^(A-4)underset(-beta)rarr ._(z-1)X^(A-4)underset(-beta)rarr ._(z)X^(A-4)`
`:.` In this series there will be three will be three different element with atomic no A, A-2, Z-1]