39. The number N of undecayed nuclei present at any time and the rate of decay R at that time are related by R = N, where is the disintegration constant. The disintegration constant is related to the half-life T1/2 by =(ln 2)/T1/2, so R =(N ln 2)/T1/2 and T1/2 =(N ln 2)/R. Since 1 5.0% by mass of the sample 147 147 is Sm, the number of Sm nuclei present in the sample is (0.150)(1.00 g) N = =6.143 × 1020 . (147 u)(1.661 × 10-24 g/u) Thus (6.143 × 1020)ln2 T1/2 = =3.55 × 1018 s =1.12 × 1011 y . 120 s-1