Maharashtra State BoardHSC Science (General) 11th
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How many particles are emitted by 0.1 g of 226Ra in one year? - Chemistry

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Numerical

How many particles are emitted by 0.1 g of 226Ra in one year?

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Solution

Given: t = 1 y, Amount of sample = 0.1 g

To find: Number of particles emitted

Formulae: 

  1. `lambda = 0.693/"t"_(1//2)`
  2. Activity = Number of α (or β) particles emitted
    `= - "dN"/"dt" = lambda"N"`

Calculation: Half-life of radium = 1620 y

`lambda = 0.693/"t"_(1//2) = 0.693/1620 = 4.28 xx 10^-4"y"^-1`

N = `(0.1 xx 6.022 xx 10^23)/226`

N = 2.665 × 1020 atoms

Activity = ` - "dN"/"dt" = lambda"N"`

= 4.28 × 10-4 × 2.665 × 1020 atoms

= 1.141 × 1017 particles/year

Particles emitted by 0.1 g of 226Ra in one year = 1.141 × 1017 particles/year.

Concept: Modes of Decay
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APPEARS IN

Balbharati Chemistry 11th Standard Maharashtra State Board
Chapter 13 Nuclear Chemistry and Radioactivity
Exercises | Q 4. (I) | Page 203
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