The half-life of radium is 1620 years and its | vedclass

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(A) The activity $R$ is given by $R = \lambda N$, where $\lambda = \frac{\ln 2}{T_{1/2}}$ and $N = \frac{m}{M} 	imes N_A$.Given:$T_{1/2} = 1620 \,

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$3.61 	imes 10^{10}$

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(A) The activity $R$ is given by $R = \lambda N$, where $\lambda = \frac{\ln 2}{T_{1/2}}$ and $N = \frac{m}{M} 	imes N_A$.Given:$T_{1/2} = 1620 \, 	ext{years} = 1620 	imes 365 	imes 24 	imes 3600 \, 	ext{seconds} \approx 5.11 	imes 10^{10} \, 	ext{s}$.$m = 1 \, 	ext{g}$, $M = 226 \, 	ext{g/mol}$, $N_A = 6.023 	imes 10^{23} \, 	ext{atoms/mol}$.Number of atoms $N = \frac{1}{226} 	imes 6.023 	imes 10^{23} \approx 2.665 	imes 10^{21} \, 	ext{atoms}$.Decay constant $\lambda = \frac{0.693}{5.11 	imes 10^{10}} \approx 1.356 	imes 10^{-11} \, 	ext{s}^{-1}$.Activity $R = \lambda N = (1.356 	imes 10^{-11}) 	imes (2.665 	imes 10^{21}) \approx 3.61 	imes 10^{10} \, 	ext{decays/s}$.

The half-life of radium is $1620$ years and its atomic weight is $226 \, g/mol$. What is the number of atoms decaying per second in a $1 \, g$ sample? $[N_A = 6.023 \times 10^{23} \, \text{atoms/mol}]$

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