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(C) The decay rate is given by $|\frac{dN}{dt}| = \lambda N$. At $t = 0$,the decay rate is $|\frac{dN}{dt}|_0 = \lambda N_0$. The initial number of at

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$\frac{0.693 M N_A}{A T}$

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(C) The decay rate is given by $|\frac{dN}{dt}| = \lambda N$. At $t = 0$,the decay rate is $|\frac{dN}{dt}|_0 = \lambda N_0$. The initial number of atoms $N_0$ is given by $N_0 = \frac{	ext{Mass}}{	ext{Molar Mass}} 	imes N_A = \frac{M}{A} N_A$. The decay constant $\lambda$ is related to the half-life $T$ by $\lambda = \frac{\ln 2}{T} \approx \frac{0.693}{T}$. Substituting these values,the initial decay rate is $|\frac{dN}{dt}|_0 = (\frac{0.693}{T}) 	imes (\frac{M N_A}{A}) = \frac{0.693 M N_A}{A T}$.

Consider an initially pure $M \text{ g}$ sample of an isotope $X$ with mass number $A$,which has a half-life of $T \text{ hours}$. What is its initial decay rate? ($N_A$ = Avogadro number)

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