The half-life of Ra^{226} is 1620 years. Calc | vedclass

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(C) The rate of decay is given by $\frac{dN}{dt} = \lambda N$,where $\lambda = \frac{0.693}{T_{1/2}}$.First,convert the half-life $T_{1/2} = 1620$ yea

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$3.61 	imes 10^{10}$

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(C) The rate of decay is given by $\frac{dN}{dt} = \lambda N$,where $\lambda = \frac{0.693}{T_{1/2}}$.First,convert the half-life $T_{1/2} = 1620$ years into seconds:$T_{1/2} = 1620 	imes 365 	imes 24 	imes 3600 \approx 5.11 	imes 10^{10} \ s$.Next,calculate the number of atoms $N$ in $1 \ g$ of $Ra^{226}$:$N = \frac{	ext{mass}}{	ext{molar mass}} 	imes N_A = \frac{1}{226} 	imes 6.023 	imes 10^{23} \approx 2.665 	imes 10^{21}$ atoms.Now,calculate the activity $\frac{dN}{dt} = \frac{0.693}{T_{1/2}} 	imes N$:$\frac{dN}{dt} = \frac{0.693}{5.11 	imes 10^{10}} 	imes 2.665 	imes 10^{21} \approx 3.61 	imes 10^{10}$ decays per second.

The half-life of $Ra^{226}$ is $1620$ years. Calculate the number of atoms that decay in one second in $1 \ g$ of radium (Avogadro number $= 6.023 \times 10^{23}$).

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