Radium has an atomic weight of 226 and a half | vedclass

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(C) The rate of disintegration $(r)$ is given by the formula $r = \lambda N$,where $\lambda = \frac{0.693}{t_{1/2}}$ and $N$ is the number of atoms.Fi

Vedclass · Accepted Answer

$3.7 	imes 10^{10}$

Vedclass · Answer

(C) The rate of disintegration $(r)$ is given by the formula $r = \lambda N$,where $\lambda = \frac{0.693}{t_{1/2}}$ and $N$ is the number of atoms.First,calculate the decay constant $\lambda$ in seconds$^{-1}$:$\lambda = \frac{0.693}{1600 	imes 365 	imes 24 	imes 60 	imes 60} \approx 1.37 	imes 10^{-11} \ s^{-1}$.Next,calculate the number of atoms $N$ in $1 \ g$ of radium:$N = \frac{	ext{mass}}{	ext{atomic weight}} 	imes N_A = \frac{1}{226} 	imes 6.023 	imes 10^{23} \approx 2.665 	imes 10^{21} \ 	ext{atoms}$.Finally,calculate the rate of disintegration $r$:$r = (1.37 	imes 10^{-11}) 	imes (2.665 	imes 10^{21}) \approx 3.65 	imes 10^{10} \ dps$.This value is approximately $3.7 	imes 10^{10} \ dps$.

Radium has an atomic weight of $226$ and a half-life of $1600$ years. The number of disintegrations produced per second from $1 \ g$ of radium is:

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