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 ____

Step-by-step solution

6 . 25 % of the initial value means, final number of nuclei should be, N 0 16 . Number of nuclei remaining after n half lives is N = N 0 2 n 6 . 25 %   N 0 = N 0 2 n 6 . 25 100 N 0 = N 0 2 n   ⇒ 625 10 4 = 1 2 n ⇒ 2 n = 10 4 5 4   ⇒ 2 n = 2 4 ⇒ n = 4 Therefore, time taken will be, n × t 1 2 = 4 × 5 = 20   y e a r s