Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 12
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212 83 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 - Physics

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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 βparticle

`""_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"`

  Is there an error in this question or solution?

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Solution 212 83 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 Concept: Radioactivity - Introduction of Radioactivity.
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