The half-life of ^{238}_{92}U undergoing alph | vedclass

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(D) The half-life $T_{1/2} = 4.5 	imes 10^{9} 	ext{ years}$.Converting to seconds: $T_{1/2} = 4.5 	imes 10^{9} 	imes 3.1536 	imes 10^{7} 	ext{ s

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$1.23 	imes 10^{4} 	ext{ Bq}$

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(D) The half-life $T_{1/2} = 4.5 	imes 10^{9} 	ext{ years}$.Converting to seconds: $T_{1/2} = 4.5 	imes 10^{9} 	imes 3.1536 	imes 10^{7} 	ext{ s} \approx 1.42 	imes 10^{17} 	ext{ s}$.The number of atoms $N$ in $1 	ext{ g}$ of $^{238}_{92}U$ is given by $N = (	ext{mass} / 	ext{molar mass}) 	imes N_A$.$N = (1 / 238) 	imes 6.022 	imes 10^{23} \approx 2.53 	imes 10^{21} 	ext{ atoms}$.The activity $R$ is given by $R = \lambda N = (0.693 / T_{1/2}) 	imes N$.$R = (0.693 	imes 2.53 	imes 10^{21}) / (1.42 	imes 10^{17}) 	ext{ s}^{-1}$.$R \approx 1.23 	imes 10^{4} 	ext{ Bq}$.

The half-life of $^{238}_{92}U$ undergoing $\alpha$-decay is $4.5 \times 10^{9} \text{ years}$. What is the activity of a $1 \text{ g}$ sample of $^{238}_{92}U$?

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