A nucleus has a half-life of 30 ; min. At 3 ; | vedclass

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(D) The half-life $(T_{1/2})$ of the nucleus is $30 \; min$. The time interval between $3 \; PM$ and $5 \; PM$ is $2 \; hours$, which is equal to $120

Vedclass · Accepted Answer

$7500$

Vedclass · Answer

(D) The half-life $(T_{1/2})$ of the nucleus is $30 \; min$. The time interval between $3 \; PM$ and $5 \; PM$ is $2 \; hours$, which is equal to $120 \; min$. The number of half-lives $(n)$ elapsed is given by $n = \frac{	ext{Total time}}{T_{1/2}} = \frac{120 \; min}{30 \; min} = 4$. The decay rate $(R)$ follows the law $R = R_0 \left( \frac{1}{2} ight)^n$, where $R_0 = 120000 \; cps$. Substituting the values, we get $R = 120000 	imes \left( \frac{1}{2} ight)^4 = 120000 	imes \frac{1}{16} = 7500 \; cps$. Thus, the decay rate at $5 \; PM$ is $7500 \; cps$.

$A$ nucleus has a half-life of $30 \; min$. At $3 \; PM$, its decay rate was measured as $120000 \; cps$. What is the decay rate in $cps$ at $5 \; PM$?

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