Question

You have created a device that can detect and count every decay even from a sample of plutonium-239. This nuclide has a half life of 24000 years. If you have a 0.385g sample of plutonium-239, how many disintegrations per second should your device count?

Answer 1

The expression that relates the activity of a sample to its initial amount is

Activity = k*Ao

where k is the rate constant and Ao is the initial amount of radioisotope.

We know that k and the half-life (t(1/2)) are related by the following expression:

k = 0.693/t(1/2) = (0.693/24000 yr) * (1 yr/365 d) * (1 d/24 h) * (1 h/3600) = 9.16 * 10^-13 s-1

and we know that the number of atoms in 0.385 g of plutonium is:

0.385 g Pu * (1 mole Pu/244 g Pu) * (6.022*10^23 atoms Pu/1 mole Pu) = 9.5 * 10^20 atoms of Pu.

Therefore, the activity will be

Activity = (9.16 * 10^-13 s-1)*(9.5 * 10^20 atoms of Pu) = 8.7 * 10^8 dps