Question

The half-life of a radioactive substance is 5 years. After x years a given sample of the radioactive substance gets reduced to 6.25% of its initial value. The value of x is ______.

Options

• 19

• 20

• 21

• 22

Answer 1

The half-life of a radioactive substance is 5 years. After x years a given sample of the radioactive substance gets reduced to 6.25% of its initial value. The value of x is 20.

Explanation:

As, `N/N_0 = [1/2]^(T/(T_{1"/"2}))`

⇒ `6.25/100 = [1/2]^(x/5)`

⇒ `1/16 = [1/2]^(x/5)`

⇒ `[1/2]^4 = [1/2]^(x/5)`

`x/5 = 4`

x = 20 years