[填空题]
A 1.00-g sample of natural sam41 zgg ryf/ku;nb),rx ariu4:fkrfdiyejt x : dvp qq5(6 k.,6cdk)m emits $\alpha$ particles at a rate of $120\ \text{s}^{-1}$ due to the presence of $_{62}^{147}\text{Sm}$. The natural abundance of $_{62}^{147}\text{Sm}$ is 15%. Calculate the half-life for this decay process.
$T_{\frac{1}{2}}$ = $ \times 10^{11}\ \text{yr}$
