There are two radio nuceli `A` and `B. A` is an `alpha` emitter and `B` a `beta` emitter. Their disintegration constant are in the ratio of `1:2` What should be the ratio of number of atoms of `A` and `B` at any time t so that probabilities of getting alpha and beta particles are same at that instant?

Options

A. `1:2`
B. `2:1`
C. `e:1`
D. `1:e`

Answer

B

Explanation

Here, `(lambda_(A))/(lambda_(B))=(1)/(2)`
As probabilities of getting alpha and beta particles are same, the rates of disintegration of the two elements are eqaul.
`therefore lambda_(A)N_(A)=lambda_(B)N_(B) or (N_(A))/(N_(B)) or (N_(A))/(N_(B))=(lambda_(B))/(lambda_(A))=(2)/(1)`
As probabilities of getting alpha and beta particles are same, the rates of disintegration of the two elements are equal.
`therefore lambda_(A)N_(A)=lambda_(B)N_(B) or (N_(A))/(N_(B))=(lambda-(B))/(lambda_(A))=(2)/(1)`