1.

32 mg of pure ._(94)^(238)PuO_(2) has an activity of 6.4 xx 10^(7) sec^(-1) (i) What will be the half life of ._(94)^(238)Pu in years? (ii) What amount of PuO_(2) will remain if 100 mg PuO_(2) is kept for 500 years?

Answer»

Solution :(i) Mass of `.^(238)Pu = (238)/(270) xx 32 = 28.207 MG`
Rate `= (0.693)/(t_(1//)) xx (w)/("At.wt") xx N`
`6.4 xx 10^(7) = (0.693)/(t_(1//2)) xx (28.207 xx 10^(-3))/(238) xx 6.023 xx 10^(23)`
`t_(1//2)= 7.729 xx 10^(11) sec = 2.45 xx 10^(4)` YEARS
(ii), `(0.693)/(t_(1//2)) = (2.303)/(t) log_(10) ((N_(0))/(N))`
`(0.693)/(2.45 xx 10^(4)) = (2.303)/(5000) log_(10) ((100)/(N))`
`N = 86.7` mg


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