The 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 formed to be 1 : 3. Half life of 'A' is 1 day. What will be the half life of B?

Options

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

Answer

a

Explanation

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