A mixture of `""^(239)Pu` and `""^(240)Pu` has an activity of `6.0 xx 10^(9)` dis/s. The half-life lives of isotopes are `2.44 xx 10^(4)` and `6.58 xx 10^(3)` years, respectively. Calculate the isotopic composition of this sample.

Options

A. `""^(239)Pu = 38.96%, ""^(240)Pu = 61.04%`
B. `""^(239)Pu = 3.89%, ""^(240)Pu = 6.14%`
C. `""^(239)Pu = 30.9%, ""^(240)Pu = 68.4%`
D. `""^(239)Pu = 0.389%, ""^(240)Pu = 0.614%`

Answer

A

Explanation

Total activity of a sample is the sum of the individual activities of all its components.
let the total mass of the sample be 1 gm and the mass of `"^(239)Pu` be .x. gm.
`(x)/(239) xx 6.02 xx 10^(23) xx (0.693)/(2.44 xx 10^(4)) + ((1-x))/(240) xx 6.02 xx 10^(23) xx (0.693)/(6.58 xx 10^(3)) = 6 xx10^(9) xx 365 xx 24 xx 60 xx 60`
On calculating, `x =0.3896 " "therefore""^(239)Pu = 38.96% and ""^(240)Pu = 61.04%`