The half-life of {}_{92}^{238}U against alpha | vedclass

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(A) The activity $R$ of a radioactive sample is given by $R = \lambda N$,where $\lambda$ is the decay constant and $N$ is the number of nuclei.Given:

Vedclass · Accepted Answer

$1.26 	imes 10^4 \,s^{-1}$

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(A) The activity $R$ of a radioactive sample is given by $R = \lambda N$,where $\lambda$ is the decay constant and $N$ is the number of nuclei.Given: Half-life $T_{1/2} = 13.86 	imes 10^{16} \,s$,mass $m = 1 \,g$,and molar mass $M = 238 \,g/mol$.The decay constant $\lambda = \frac{\ln(2)}{T_{1/2}} \approx \frac{0.693}{T_{1/2}}$.The number of nuclei $N = \frac{m}{M} 	imes N_A$,where $N_A = 6.022 	imes 10^{23} \,mol^{-1}$.Substituting the values:$R = \frac{0.693}{13.86 	imes 10^{16}} 	imes \frac{1}{238} 	imes 6.022 	imes 10^{23}$$R = \frac{0.693 	imes 6.022}{13.86 	imes 238} 	imes 10^7$$R = \frac{4.173}{3298.68} 	imes 10^7 \approx 0.001265 	imes 10^7 = 1.265 	imes 10^4 \,s^{-1}$.Thus,the activity is approximately $1.26 	imes 10^4 \,s^{-1}$.

The half-life of ${}_{92}^{238}U$ against $\alpha$-decay is $13.86 \times 10^{16} \,s$. The activity of a $1 \,g$ sample of ${}_{92}^{238}U$ is:

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