Question

A fraction $f_{1}$ of a radioactive sample decays in one mean life, and a fraction $f_{2}$ decays in one half life. Then

• A. $f_{1} > f_{2}$
• B. $f_{1} < f_{2}$
• C. $f_{1} = f_{2}$
• D. Either of (1), (2) or (3) depending on the values of the mean life and half life

Answer 1

Answer: (A)

$f_{1} > f_{2}$

Answer 2

: Mean life, $\tau = \frac{1}{\lambda}$

And half life , $T_{1/2} = \frac{\ln 2}{\lambda} = \frac{0.693}{\lambda}$

$\because\tau > T_{1/2}$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.

$f_{1} > f_{2}$