Answer
621
Work Step by Step
Decay constant $k=\frac{0.693}{t_{1/2}}=\frac{0.693}{102\times365\times24\times60\times60\,s}=2.1544\times10^{-10}\,s^{-1}$
Number of moles $n=\frac{\text{mass in grams}}{\text{molar mass}}=\frac{1.0\times10^{-9}\,g}{209\,g/mol}=4.7847\times10^{-12}\,mol$
Number of particles $N=n\times\text{Avogadro number}$
$=4.7847\times10^{-12}\times 6.022\times10^{23}=2.881346\times10^{12}$
Decay rate=$kN=2.1544\times10^{-10}\,s^{-1}\times2.881346\times10^{12}=621\text{ emissions per second}$
