1.

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

Answer»

Solution :Specific activity means activity per gram. Sp. Activity of `""^(239)Pu= lamda= N = ((0.6932)/(2.44 xx 10^(4))) ((6.022 xx 10^(23))/(239))`
`=7.15 xx 10^(16)`/YR/g
`=2.27 xx 10^(9)//s//g. (1 yr = 3.15 xx 10^(7)s)`
Sp. activity of `""^(240)Pu= ((0.6932)/(6.58 xx 10^(3))) ((6.022 xx 10^(23))/(240))`
`=2.64 xx 10^(17)//yr//g= 8.37 xx 10^(9)//s//g`
THUS, `(2.27 xx 10^(9)) x + (8.37 xx 10^(9)) (1-x)=6.0 xx 10^(9)` (x=fraction of `""^(239)Pu`) x=0.39 or 39%


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