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, ${\displaystyle \frac{N}{N_0}={\left[\frac{1}{2}\right]}^{\frac{T}{T_{1\text{/}2}}}}$

⇒ ${\displaystyle \frac{6.25}{100}={\left[\frac{1}{2}\right]}^{\frac{x}{5}}}$

⇒ ${\displaystyle \frac{1}{16}={\left[\frac{1}{2}\right]}^{\frac{x}{5}}}$

⇒ ${\displaystyle {\left[\frac{1}{2}\right]}^4={\left[\frac{1}{2}\right]}^{\frac{x}{5}}}$

${\displaystyle \frac{x}{5}=4}$

x = 20 years