Answer
$m = 8.36\times 10^{-8}~kg$
Work Step by Step
We can write an expression for the decay rate:
$r = \frac{ln~2}{t_{1/2}}$
We can find the number of atoms $N$:
$R = r~N$
$R = (\frac{ln~2}{t_{1/2}})~(N)$
$N = \frac{R~t_{1/2}}{ln~2}$
$N = \frac{(3.50\times 10^9)(5.27)(365)(24)(3600)}{ln~2}$
$N = 8.39\times 10^{17}~atoms$
We can find the mass:
$m = (8.39\times 10^{17}~atoms)(60)(1.66\times 10^{-27}~kg)$
$m = 8.36\times 10^{-8}~kg$
