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

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(C) The number of atoms decaying per second is given by the activity $A = \lambda N$.First,calculate the decay constant $\lambda = \frac{0.693}{T_{1/2

Vedclass · Accepted Answer

$3.61 	imes 10^{10}$

Vedclass · Answer

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

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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