Atoms and Nuclei Problems - Numerical 12

12.

The half-life of ₉₂U²³⁸ against alpha decay is 4.5 x 109 years. How many disintegrations per second occur in 1 g of ₉₂U²³⁸ ?

Suggested solution:

Again, since one k mole of any isotope contains Avogadro's number of atoms, there fore 1 g of ₉₂U²³⁸ contains

Half life T = 4.5 10⁹ years

Again, since one k mole of any isotope contains Avogadro's number of atoms, therefore 1g of ₉₂U²³⁸ contains,

= 4.20 x 10^-6k mole x 6.025 x 10²⁶ atoms / k mole

= 25.3 x 10²⁰ atoms

Decay rate,

= 1.23 x 10⁴ s^-1