Question

$15/{16}^{th}$ of a radioactive sample disintegrates in $2hrs$. Mean life of radioactive sample is approximately.

• A. $30min$
• B. $43min$
• C. $21min$
• D. $15min$

Answer 1

The correct option is B $43min$

Mean life $\tau =1.44t_{1/2}$

where $t_{1/2}$ is Half life time

$N\left(t\right)=N_o(1/2{)}^{\frac{t}{t_{1/2}}}$

Above equation can be written as $t_{1/2}=\frac{t\ln 2}{\ln \left(N_o/N\right(t\left)\right)}$

Given $N\left(t\right)=\frac{N_o}{16}$ and $t=2hrs$

Substituting in above equation

$t_{1/2}=\frac{2\ln 2}{\ln \left(16\right)}$

$\Rightarrow t_{1/2}=\frac{2\ln 2}{4\ln 2}$

$\Rightarrow t_{1/2}$ = (1/2)hr or 30min

$\therefore \tau =1.44\times 30=43.2min$