Question

A sample initially contains 1020 radioactive atoms of half-life 130 days. Calculate the activity of the sample after 260 days have elapsed. Also find the total energy released during this ** if the energy released per disintegration is 8 × 10–13 J.

In 260 days, i.e., two half-lives, the number of undisintegrated atoms will reduce to 1/4th.

Answer 1

∴ no. of atoms present after 260 days = N = 1/4 × 1020

Also, disintegration constant = λ = 0.6931/T

where T = 130 days = 130 × 86400 *

Now, activity = λN = 0.693 0.693 130 x 86400 × 1/4 × 1020 = 1.54 × 1012 *

Number of atoms present initially= 1020

Number of atoms present after 260 days = 1/4 × 1020

∴ number of disintegrated atoms = 3/4 × 1020

Energy per disintegration = 8 × 10–13 J

∴ total energy released = 3/4 × 1020× 8 × 10 –13 = 6 × 107 J.