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# A radioactive substance has density $\rho$ , volume V, and decay constant $\lambda$. If the molecular weight of the substance is M, and Avogadro number is $N_a$ then the radioactivity of the substance after time 't' is

$\begin {array} {1 1} (1)\;\bigg( \large\frac{\lambda\: V \rho\: N_a}{M}\bigg) ( 1-e^{-\lambda\: t}) & \quad (2)\;\bigg( \large\frac{tN_aV}{\rho\: M}\bigg)e^{-\large\frac{\lambda\: t}{2}} \\ (3)\;\large\frac{\lambda\: N_a}{V \: \rho\: M}e^{-\lambda\: t} & \quad (4)\;\large\frac{\lambda\: V\: \rho\:N_a\: e^{-\lambda\: t}}{M} \end {array}$

(4) $\large\frac{\lambda\: V\: \rho\:N_a\: e^{-\lambda\: t}}{M}$