Question

The half life of a radioactive substance is 20 minutes. In how much time, the activity of substance drops to (1/16)^th of its initial value ?

(1) 40 minutes

(2) 60 minutes

(3) 80 minutes

(4) 20 minutes

Answer 1

Correct option is (3) 80 minutes

Half life T = 20 min

Left fraction of activity \(\frac{1}{16}\)

∵ \(\frac{R}{R_0}=(\frac{1}{2})^{t/2}\)

\(\frac{1}{16}\) = \((\frac{1}{2})^{t/20}\)

\((\frac{1}{2})^{4}\) = \((\frac{1}{2})^{t/20}\)

4 = \(\frac{t}{20}\)

t = 80 min