Question

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

Answer 1

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.