The half-life of a radioactive substance agai | vedclass

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(D) The decay rate (activity) is given by the formula: $\left| \frac{dN}{dt} \right| = \lambda N$. Here,$\lambda$ is the decay constant,which is relat

Vedclass · Accepted Answer

$2.3 	imes 10^8 \ 	ext{atoms/s}$

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(D) The decay rate (activity) is given by the formula: $\left| \frac{dN}{dt} ight| = \lambda N$. Here,$\lambda$ is the decay constant,which is related to the half-life $T_{1/2}$ by $\lambda = \frac{0.693}{T_{1/2}}$. Given: $T_{1/2} = 1.2 	imes 10^7 \ s$ and $N = 4 	imes 10^{15}$ atoms. Substituting these values: $\left| \frac{dN}{dt} ight| = \frac{0.693}{1.2 	imes 10^7} 	imes 4 	imes 10^{15}$. $\left| \frac{dN}{dt} ight| = \frac{0.693}{1.2} 	imes 4 	imes 10^8$. $\left| \frac{dN}{dt} ight| = 0.5775 	imes 4 	imes 10^8 = 2.31 	imes 10^8 \ 	ext{atoms/s}$. Thus,the decay rate is approximately $2.3 	imes 10^8 \ 	ext{atoms/s}$.

The half-life of a radioactive substance against $\alpha$-decay is $1.2 \times 10^7 \ s$. What is the decay rate for $4 \times 10^{15}$ atoms of the substance?

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