Question

What is the half-life period of a radioactive material if its activity drops to 1/16^th of its initial value of 30 years?

Options

• 9.5 years

• 8.5 years

• 7.5 years

• 10.5 years

Answer 1

7.5 years

Explanation:

The activity is given as,

A = A_o e^-λt

⇒ -λt = ln `("A"/"A"_"o")`

⇒ `ln 2/"t"_(1//2)xx30=ln(1/16)`

⇒ `ln 2/"t"_(1//2)xx30=(ln2)xx-4`

⇒ t_1/2 = `30/4`

= 7.5 years