Answer
$6.34\times10^{11}$
Work Step by Step
Decay constant $k=\frac{0.693}{t_{1/2}}=\frac{0.693}{433\times365\times24\times60\times60\,s}=5.075\times10^{-11}\,s^{-1}$
Number of moles $n=\frac{\text{mass in grams}}{\text{molar mass}}=\frac{5.0\,g}{241\,g/mol}=0.020747\,mol$
Number of particles $N=n\times\text{Avogadro number}$
$=0.020747\times 6.022\times10^{23}=1.2494\times10^{22}$
Decay rate=$kN=5.075\times10^{-11}\,s^{-1}\times1.2494\times10^{22}$
$=6.34\times10^{11}\text{ emissions per second}$
