A heavy nucleus Q of half-life 20 minutes und | vedclass

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Question

Out of 1000 nuclei of Q $60 \%$ may go $\alpha$-decay

$\Rightarrow 600$ nuclei may have $\alpha$-decay

$\lambda=\frac{\ln 2}{t_{1 / 2}}=\frac{\l

Vedclass · Accepted Answer

$525$

Vedclass · Answer

Out of 1000 nuclei of Q $60 \%$ may go $\alpha$-decay

$\Rightarrow 600$ nuclei may have $\alpha$-decay

$\lambda=\frac{\ln 2}{t_{1 / 2}}=\frac{\ln 2}{20}$

$t =1 	ext { hour }=60 	ext { minutes }$

Using

$N  = N _0 e ^{-\lambda t}$

$=600 	imes e ^{-\frac{\ln 2}{20} 	imes 60}$

$N  =75$

$\Rightarrow \quad 75$ Nuclei are left after one hour

So, No. of nuclei decayed

$=600-75=525$

A heavy nucleus $Q$ of half-life $20$ minutes undergoes alpha-decay with probability of $60 \%$ and beta-decay with probability of $40 \%$. Initially, the number of Q nuclei is $1000$ . The number of alphadecays of $Q$ in the first one hour is

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