A heavy nucleus Q of half-life 20 minutes undergoes alpha-decay with probability of 60 % and beta-de

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13.Nuclei

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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

$50$

$75$

$350$

$525$

(IIT-2021)

Out of 1000 nuclei of Q $60 \%$ may go $\alpha$-decay

$\Rightarrow 600$ nuclei may have $\alpha$-decay

$\lambda=\frac{\ln 2}{t_{1 / 2}}=\frac{\ln 2}{20}$

$t =1 \text { hour }=60 \text { minutes }$

Using

$N = N _0 e ^{-\lambda t}$

$=600 \times e ^{-\frac{\ln 2}{20} \times 60}$

$N =75$

$\Rightarrow \quad 75$ Nuclei are left after one hour

So, No. of nuclei decayed

$=600-75=525$

Standard 12

Physics

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medium

medium

medium

easy

(AIPMT-2010)