Question

Bi21283 can disintegrate either by emitting an α-particle of by emitting a β−-particle. (a) Write the two equations showing the products of the decays. (b) The probabilities of disintegration α-and β-decays are in the ratio 7/13. The overall half-life of 212Bi is one hour. If 1 g of pure 212Bi is taken at 12.00 noon, what will be the composition of this sample at 1 P.m. the same day?

Answer 1

Answer:

It is given:

• 212Bi has the half-life, T1/2 = 1 h-1

• When there is a disintegration of Bi83212 because of an α-particle’s emission,

• $\mathrm{Bi} 83212 \div \mathrm{He} 24(\mathrm{a})+\mathrm{T} 812081$
• When there is a disintegration of Bi83212 after emitting the beta particle,  
• $\mathrm{Bi} 83212 \rightarrow+\beta-+\mathrm{PO} 84212+\mathrm{v}^{-}$

• 212Bi has the half-life period, T12 = 1 h -1

• 212Bi present at t = 0 = 1 g

• At t = One half-life = 1,

• The presence of 212Bi = 0.5 g

• Disintegration probability of β-decay and α-decay are in the ratio

• 713.
• The amount of 208Ti in 20 g of 212Bi = 7 g

• The amount of 208Ti in 1 g of 212Bi = 7/20 g

• Therefore, in 0.5 grams, the amount of 208Ti present =

• $720 \times 0.5=0.175 \mathrm{g}$

• The amount of 212Po formed in 20 g of 212Bi = 13 g

• The amount of 212Po formed in 1 g of 212Bi = 13/20 g

• Therefore, in 0.5 grams, the amount of $212 \mathrm{Po}=1320 \times 0.5=0.325 \mathrm{g}$