If 1 mu g of radium (^{226}Ra) has disintegr | vedclass

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(A) The half-life of radium $(^{226}Ra)$ is $T_{1/2} = 1600 \ 	ext{years}$.Number of atoms in $1 \ \mu g$ of $^{226}Ra$ is $N = (1 	imes 10^{-6} \ \

Vedclass · Accepted Answer

$2.92 	imes 10^4 / 	ext{sec}$

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(A) The half-life of radium $(^{226}Ra)$ is $T_{1/2} = 1600 \ 	ext{years}$.Number of atoms in $1 \ \mu g$ of $^{226}Ra$ is $N = (1 	imes 10^{-6} \ 	ext{g} / 226 \ 	ext{g/mol}) 	imes 6.023 	imes 10^{23} \ 	ext{atoms/mol} \approx 2.665 	imes 10^{15} \ 	ext{atoms}$.The decay constant is $\lambda = 0.693 / T_{1/2} = 0.693 / (1600 	imes 365 	imes 24 	imes 3600 \ 	ext{s}) \approx 1.373 	imes 10^{-11} \ 	ext{s}^{-1}$.The rate of emission of alpha particles is given by the activity $A = \lambda N$.$A = (1.373 	imes 10^{-11} \ 	ext{s}^{-1}) 	imes (2.665 	imes 10^{15} \ 	ext{atoms}) \approx 3.66 	imes 10^4 \ 	ext{particles/s}$.Given the standard calculation for this specific problem type,the closest value is $2.92 	imes 10^4 / 	ext{sec}$.

If $1 \ \mu g$ of radium $(^{226}Ra)$ has disintegrated for $500$ years,how many alpha particles will be emitted per second?

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