The nuclide ²¹²₈₃ Bi is capable of disintegrating by emitting either an -particle or a ⁻ -particle. The probabilities for disintegration via - and -decays stand in the ratio 7/13 . The overall half-life of ²¹²₈₃ Bi is one hour. Suppose 1 g of pure ²¹²₈₃ Bi is taken at 12.00 noon. Determine the composition of this sample at 1 p.m. on the same day.

Step-by-step solution

The initial mass of ²¹²₈₃ Bi is 1 g . The overall half-life of ²¹²₈₃ Bi is 1 hour . Since the time elapsed from 12.00 noon to 1 p.m. is exactly 1 hour (one half-life), the amount of ²¹²₈₃ Bi remaining is: W_ Bi = 1 ( 1 2 )^1 = 0.50 g The mass of ²¹²₈₃ Bi that has decayed is: W_ decayed = 1 - 0.50 = 0.50 g The decay occurs via two parallel pathways: -decay: ²¹²₈₃ Bi ²⁰⁸₈₁ Tl + ⁴₂ He -decay: ²¹²₈₃ Bi ²¹²₈₄ Po + ⁻ The probabilities for - and -decays are in the ratio 7/13 . Therefore, the fractions of the decayed ²¹²₈₃