Question

A sample $Q$ has half life $20\text{min}$. It decays by emitting alpha particle and beta particle with probability of $60\%$ and $40\%$ respectively.
Initial sample of $Q$ contains $1000$ nuclei, then number of $\alpha -$ particle decay after one hour will be

• A. $350$
• B. $75$
• C. $50$
• D. $525$

Answer 1

The correct option is D $525$

Out of $1000$ nuclei of $Q$ $60\text{\%}$ may go $\alpha -$decay
$\Rightarrow 600$ nuclei may have $\alpha -$decay
$\Rightarrow \lambda =\frac{\ln 2}{t_{\frac{1}{2}}}=\frac{\ln 2}{20}$
Given, $t=1\text{hour}=60\text{min}$
Using,
$N=N_0{e}^{-\lambda t}=600\times e^{-\left(\frac{\ln 2}{20}\right)\times 60}$
$\Rightarrow N=75$
Thus, $75$ Nuclei are left after one hour
So, no. of nuclei decayed
$=600-75=525$