1.

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 ?

Answer»

0.03087 , 0.00063
0.00063 , 0.03087
0.02 , 0.98
none of these

Solution :`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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