Question:
A radioactive nucleus decays by two different processes. The half life for the first process is $10 \mathrm{~s}$ and that for the second is $100 \mathrm{~s}$. the effective half life of the nucleus is close to:
Correct Option: 1,
Solution:
$\frac{1}{\mathrm{~T}_{\text {eff }}}=\frac{1}{\mathrm{~T}_{1}}+\frac{1}{\mathrm{~T}_{2}}$
$\mathrm{T}_{\mathrm{eff}}=\frac{\mathrm{T}_{1} \mathrm{~T}_{2}}{\mathrm{~T}_{1}+\mathrm{T}_{2}}=\frac{1000}{110}=\frac{100}{11}=9.09$
$\mathrm{T}_{\mathrm{eff}} \cong 9$