The activity of a radioactive sample is measured as `9750` counts per minute at `t = 0` and as `975` counts per minute at `t = 5` minutes. The decay constant is approximately

Options

A. `0.922"min"^(-1)`
B. `0.691"min"^(-1)`
C. `0.461"min"^(-1)`
D. `0.230"min"^(-1)`

Answer

D

Explanation

Half-time, `tau_(1//2)=(0.693)/(lamda)`
Activity, `l_(1)=N_(1)lamda and l_(2)=N_(2)lamda`
where, `lamda` disintegration constant
`therefore (l_(1)-l_(2))=(N_(1)-N_(2))(0.693)/(tau_(1//2))`
or `(N_(1)-N_(2))prop(l_(1)-l_(2))tau_(1//2)`