Question

Two different radioactive elements with half lives T₁ and T₂ have N₁ and N₂ undecayed atoms respectively present at a given instant. Derive an expression for the ratio of their activities at this instant in terms of N₁ and N_{2 ?}

Answer 1

Activity for a radioactive substance is given as

\[A = \frac{d N}{d t} = \lambda N = \frac{0 . 693N}{T}\]

\[ \therefore A_1 = \frac{0 . 693 N_1}{T_1}; A_2 = \frac{0 . 693 N_2}{T_2}\]

\[ \Rightarrow \frac{A_1}{A_2} = \frac{N_1}{T_1} \times \frac{T_2}{N_2}\]

\[ \Rightarrow \frac{A_1}{A_2} = \frac{N_1}{N_2} \times \frac{T_2}{T_1}\]