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 ______.

Answer 1

The correct answer is 20
N = N 0e–λ t
$⇒ \frac{6.25}{100} = e^{-λt}$
$⇒ e^{-λt} = \frac{1}{16} = (\frac{1}{2})^4$
⇒ t = 4 t 1/2
⇒ t = 20 years