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Question
`""_83^212"Bi"` 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?
Solution
Given:-
Half-life of `""^212"Bi" , T_"1/2" = 1 "h"^-1`
When `""_83^212"Bi"` disintegrates by emitting an α-particle
`""_83^212"Bi" → ""_81^208"T1" + ""_2^4"He"(alpha)`
When `""_83^212"Bi"` disintegrates by emitting a β−particle
`""_83^212"Bi" → ""_84^212P_0 + β^(-)+ bar"v"`
Half-life period of 212Bi, `T_(1/2)`= 1 `"h"^-1`
At t = 0, the amount of 212Bi present = 1 g
At t = 1 = One half-life,
Amount of 212Bi present = 0.5 g
Probability of disintegration of α-decay and β-decay are in the ratio `7/13`.
In 20 g of 212Bi, the amount of 208Ti formed = 7 g
In 1 g of 212Bi, the amount of 208Ti formed = 7/20 g
∴ Amount of `""^208"Ti"` present in `0.5 "g" = 7/20 xx 0.5 = 0.175 "g"`
In 20 g of 212Bi, the amount of 212Po formed = 13 g
In 1 g of 212Bi, the amount of 212Po formed = 13/20 g
∴ Amount of `""^212"Po"` present in `0.5 "g" = 13/20 xx 0.5 = 0.325 "g"`
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