A fraction `f_(1)` of a radioactive sample decays in one mean lie and a fraction `f_(2)` decays in one half-life

Options

A. `f_(1) gt f_(2)`
B. `f_(1) lt f_(2)`
C. `f_(1)=f_(2)`
D. may be (a), (b) or (c ) depending on the values of the mean life and half life.

Answer

A

Explanation

Mean life, `tau=(1)/(lambda)`
and half life, `T_(1//2)=(ln2)/(lambda)=(0.693)/(lambda)`
`because" "tau gt T_(1//2)`. Greater fraction will decay in longer time.
Hence, fraction decayed in one mean life must be greater than the fraction decayed in one half life i.e. `f_(1) gt f_(2)`.