Question

A given number of atoms, N₀ of a radioactive element with a half life T is uniformly distributed in the blood stream of a

(i) normal person A having total volume V of blood in the body

(ii) person B in need of blood transfusion having a volume V' of blood in the body.

The number of radioactive atoms per unit volume in the blood streams of the two persons after a time nT are found to be N₁ and N₂.Prove mathematically that the additional volume of blood that needs to be transfused in the body of person B equal (N₂ - N₁ / N₂)V

Answer 1

Initial number of radioactive atoms, per unit volume, in the blood streams of persons A and B are (N₀ /V and (N₀ /V))respectively. After a time nT (T = Half -life), these numbers would get reduced by a factor 2ⁿ