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