The rate of radioactive disintegration at an instant for a radioactive sample of half life 2.2 10^9 ~s is 10¹⁰ ~s ⁻¹ . The number of radioactive atoms in that sample at that instant is

Step-by-step solution

Given, half life T_ 1 / 2 =2.2 10^9 ~s Rate of disintegration, R=10¹⁰ ~s ⁻¹ If N be the number of nuclei present, then the rate of disintegration is aligned dN dt = N ( = decay constant ) R = N or N = R (i) aligned Also, the half life is given by, T _ 1 / 2 = 0.693 = 0.693 ~T _ 1 / 2 From Eq. (i) and (ii), we get N = R 0.693 T _ 1 / 2 = 10¹⁰ 2.2 10^9 0.693 =3.17 10¹⁹