Two radioactive isotopes A and B of atomic mass X and Y are mixed in equal amount by mass. After 20 days, their mass ratio is found to be 1: 4. Half life of 'A' is 1 day. What will be the half life of B ?

Options

A. 1.11 day
B. 0.6237 day
C. `0.11 (X)/(Y)` day
D. `1.11 (Y)/(X)` day

Answer

A

Explanation

Let 1 g of both A and B are the taken initially, `W_(A)` and `W_(B)` ar the amounts left after 20 days.
`lambda_(A) = (2.303)/(20) log ""(1)/(W_(A)), " "lambda_(A) = (2.303)/(20) log "" (1)/(W_(B))`
`lambda_(A) - lambda_(B) = (2.303)/(20) log "" (W_(B))/(W_(A)) = (2.303)/(20) log 4 = 0.0693`
`lambda_(B) = lambda_(A) -0.0693 = (0.693)/(t_(1//2)) - 0.0693 = (0.693)/(1) - 0.0693 = 0.6237`
`t_(1//2) "of B" = (0.693)/(0.6237) = 1.11` day