A mixture of `Pu""^(239)` and `Pu""^(240)` has specific activity of `6xx10""^(9)`dps. The half lves of isotopes are `2.44xx10""^(4)` and `6.58xx10""^(3)`years respectively. The percent of `Pu""^(239)` in the mixture is x/10% (nearly). Then 'x' is

Answer

39

Explanation

Specific activity of `Pu^(239)`
`= lambda N = (0.693)/(t_(1//2)) xx 1/(239) xx 6.02 xx 10^(23)`
Specific activity of `Pu^(240) = (0.693)/(t_(1//2)) xx 1/(240) xx 6.02 xx 10^(23)`
Let fraction of `Pu^(239) = x " "`fraction of `Pu^(240)= 1 - x `
Specific activity of the mixture = `x xx ` specific activity of
`Pu^(239) + (1-x) xx ` specific activity of `Pu^(240)`
`6 xx 10^9 = x xx (0.693 xx 6.02 xx 10^(23))/(2.44xx10^4 xx 365 xx 24 xx 60 xx 60) xx 1/(239) + ( 0.693 xx (1-x)xx 6.02 xx 10^(23))/(6.58 xx 10^3 xx 365 xx 24 xx 60 xx 60) xx 1/(240)`
`= 2.268 xx 10^9 x + (1-x) xx 8.377 xx 10^9`
`6 = 2.268 x + (1-x) xx 8.377 implies x = 0.39 = 39%`