The half-life of radium is 1620  years and its atomic weight is 226. The number of atoms that will decay from its 1 g sample per second will be:

According to avogadro's hypothesis.

${\mathrm{N}}_0=\frac{6.02 \mathrm{x} {10}^{23}}{226}=2.66 \mathrm{x} {10}^{21}$

$\mathrm{Half}-\mathrm{life}=\mathrm{T}=\frac{0.693}{\mathrm{\lambda }}=1620 \mathrm{years}$

$$\begin{gathered} \therefore \mathrm{\lambda }=\frac{0.6931}{1620 \mathrm{x} 3.16 \mathrm{x} {10}^7} \\ =1.35 \mathrm{x} {10}^{-11}{\sec }^{-1} \end{gathered}$$

Because half-life is very much large as compared to its time interval, hence

$$\begin{gathered} \mathrm{N}={\mathrm{N}}_0 \\ \mathrm{Now} \frac{\mathrm{dN}}{\mathrm{dt}}={\mathrm{\lambda N}}_0 \\ \mathrm{or} \mathrm{dN}={\mathrm{\lambda N}}_0\mathrm{dt} \\ =(1.35 \mathrm{x} {10}^{-11})(2.66 \mathrm{x} {10}^{21}) \mathrm{x} 1 \\ =3.61 \mathrm{x} {10}^{10} \end{gathered}$$