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

`""^(227)Ac` has a half-life of 22 years with respect to radioactive decay. The decay follows two prallel paths : `""^(227)Ac to ""^(227)Th " and "^(227)Ac to ""^(223)Fr.` If the percentage of the two daughter nuclides are 2.0 and 98.0, respectively, the decay constant (in `"year"^(-1)`) for `""^(227)Ac to ""^(227)Th` path is closest to

A

`6.3xx10^(-2)`

B

`6.3xx10^(-3)`

C

`6.3xx10^(-1)`

D

`6.3xx10^(-4)`

Text Solution

Verified by Experts

The correct Answer is:
D

`% Th=(R_(1))/(R_(T))=(2)/(100)`
`%Ac=(R_(2))/(R_(T))=(98)/(100)`
`:. (R_(1))/(R_(2))=(2)/(98)`
`R_(T)=R_(1)+R_(2)`
`(0.693)/(22)=R_(1)+(98)/(2)R_(1)`
`:. R_(1)=6.3xx10^(-4)`
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