Two different radioactive elements with half lives T 1 and T 2 have undecayed atoms N 1 and N 2 respectively, present at a given instant. The ratio of their activities at this instant is

Question

Two different radioactive elements with half lives T 1 ​ and T 2 ​ have undecayed atoms N 1 ​ and N 2 ​ respectively, present at a given instant. The ratio of their activities at this instant is

TestHub · Accepted Answer

Activity of a radioactive element is given by $A = λ N$

The decay constant $λ$ is related to half-life $T$ as $λ = \frac{ln 2}{T}$

For the first element, activity $A_{1} = \frac{ln 2}{T _{1}} N_{1}$

For the second element, activity $A_{2} = \frac{ln 2}{T _{2}} N_{2}$

The ratio of their activities is $\frac{A _{1}}{A _{2}} = \frac{\frac{ln 2}{T _{1}} N _{1}}{\frac{ln 2}{T _{2}} N _{2}} = \frac{N _{1} T _{2}}{N _{2} T _{1}}$

Answer: $\frac{N _{1} T _{2}}{N _{2} T _{1}}$

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