Question

A certain element decays in two different ways - it shows alpha decay with a half life of (ln 2) years and with beta decay, it has a half life of (ln 4) years. After how many years will a pure sample of 100 mg of the element would have 50 mg of that element?

विकल्प

• 0.52 years

• 0.46 years

• 0.75 years

• 1.25 years

Answer 1

0.52 years

Explanation:

For the given material, we may write

`"dN"/"dt"` = (λ₁ + λ₂)N

Hence, λ₁ + λ₂ = λ

And Since λ = `("In"  2)/"t"_(1/2)`

`("In"  2)/"t"_(1/2) = ("In"  2)/"t"_(1/2|1) +("In"  2)/"t"_(1/2|2)`

= `("In"  2)/("In"  2) +("In"  2)/("In"  4)`

= `3/2`

Hence, `"t"_(1/2)=2/3`In 2

= `2/3xx0.7`

= 0.46 years.