147 62 Sm undergoes alpha decay with a halflife of 106 1011

147 62 Sm undergoes alpha decay with a half-life of 1.06 × 1011 y. The natural abundance of 147 62 Sm is 14.97%. This means that a sample of Sm as found in nature contains 14.97% 147 62 Sm by weight. If we have a 1.67 -g sample of Sm, how many alpha particles does it emit per second?

Solution

Weight of ¹⁴⁷Sm₆₂ in natural Sm = 1.67*0.1497 = 0.249999 gms

Atomic weight of Sm = 147 gms

Number of Sm-147 atoms = 6.02x10²³ x0.249999/147

                                     = 1.024e21

Half-life of Sm-147   T_1/2 = 1.06e11 Yrs

Decay constant = 0.693/ T_1/2  = 0.693/(1.06e11 *365*24*3600)

                                  = 2.073e-19 decays/s

Sm-147 decays per second = number present x decays constant

                                          = 1.024e+21 x2.073e-19

Alpha particle emitted per second = 212