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Ac^(227) has a half - life of 22 years ....

`Ac^(227)` has a half - life of 22 years . The decay follows two parallel paths . What are the decay constants `(lambda)` for Th and Fr respectively ?

A

0.03087 , 0.00063

B

0.00063 , 0.03087

C

0.02 , 0.98

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
`Y_(th) = (lambda_(1))/(lambda) xx 100 = 2 ……. (1) , Y_(Fr) = (lambda_2)/(lambda) xx 100 = 98 ……. (2)`
`lambda _(2) = (98 lambda_(1))/(2), (lambda_(1))/(lambda_(2)) = (2)/(98) ….. (1) & lambda = (lambda_(1) + lambda_(2)) = (0.693)/(22) ….. (2) , (1) & (2)`
`lambda_(1) + (98 lambda_1)/(2) = (0.693)/(22) , (2 lambda_(1) + 98 lambda_(1))/(2) = (0.693)/(22) , (100 lambda_(1))/(2) = (0.693)/(22) implies lambda_(1) = (0.693)/(100) = 0.00063` years
but `(lambda_(1))/(lambda_(2)) = (2)/(98) , lambda = (98 lambda_(1))/(2) = 49 lambda_1 = 49 xx 0 .00063 ` = 0.03087 years
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