Answer
63 years.
Work Step by Step
Number of moles $n=\frac{\text{mass in grams}}{\text{molar mass}}=\frac{1.0\times10^{-9}\,g}{44\,g/mol}=2.2727\times10^{-11}\,mol$
Number of particles $N=n\times\text{Avogadro number}$
$=2.2727\times10^{-11}\times6.022\times10^{23}=1.3686\times10^{13}$
Decay rate= $4.8\times10^{3}\,dps=kN=k\times1.3686\times10^{13}$
$\implies$ Rate constant $ k=\frac{4.8\times10^{3}/s}{1.3686\times10^{13}}=3.507\times10^{-10}\,s^{-1}$
$t_{1/2}=\frac{0.693}{k}=\frac{0.693}{3.507\times10^{-10}\,s^{-1}}=1.976\times10^{9}\,s$
$=1.976\times10^{9}\,s\times\frac{1\,h}{3600\,s}\times\frac{1\,d}{24\,h}\times\frac{1\,y}{365\,d}=63\,y$