[填空题]
A 1.00-g sample of natural samarium e:zo9v hn7a l8ymits gx pm1 ut/vbp 84sp djcc*c1 j2u95tb9$\alpha$ 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}$
