The activity of a freshly prepared radioactive sample of a radioisotope is 10¹⁰ disintegrations per second. The average life ( ) of this isotope is 10^9 s , and the mass of a single atom of this isotope is 10⁻²⁵ kg . The total mass of the radioactive sample is

Step-by-step solution

The activity of a radioactive sample is given by A = N , where is the decay constant and N is the number of active nuclei. The average life is related to the decay constant by = 1 . Substituting = 1 into the activity equation, we get: A = N N = A Given A = 10¹⁰ s ⁻¹ and = 10^9 s , the number of atoms is: N = 10¹⁰ 10^9 = 10¹⁹ The total mass M of the radioactive sample is the product of the number of atoms and the mass of a single atom m : M = N m Given m = 10⁻²⁵ kg , we have: M = 10¹⁹ 10⁻²⁵ kg = 10⁻⁶ kg Converting t