Question

A radioactive nucleus can decay in two different processes with half life $0.7hr$ and $0.3hr$. The effective average life of the nucleus in minutes approximately is (value of $\ln 2=0.7)$

• A. 14
• B. 18
• C. 24
• D. 26

Answer 1

Answer: (B)

If a radioactive sample has more than one radioactive material then the effective half life.
$\frac{1}{T_{\text{eff }T/2}}=\frac{1}{T_{1\frac{1}{2}}}+\frac{1}{T_{2\frac{1}{2}}}+\frac{1}{T_{3\frac{1}{3}}}+\dots$
Where, $T_{n\frac{1}{2}}=$ half life of $n^{\text{th }}$ material.
Here, effective half life of the net material,
$T_{\text{eff }\frac{1}{2}}=\frac{0.7\times 0.3}{0.7+0.3}=0.21hr$
$\left(\because T_{1\frac{1}{2}}=0.7hr,T_{2\frac{1}{2}}=0.3hr\right)$
As we know, $T_{1/2}=0.693{\tau }_{\text{aveg. mean life }}$
$\Rightarrow {\tau }_{\text{aveg. mean life }}=\frac{T_{\text{eff }\frac{1}{2}}}{0.693}$ $=\frac{0.21}{0.693}=0.3hr$
$\Rightarrow {\tau }_{\text{aveg. mean life }}=0.3\times 60=18min$