Define the term ‘Half-life’ of a radioactive substance. Two different radioactive substances have half-lives T1 and T2 and number of un decayed atoms at an instant, N1 and N2 , respectively. Find the ratio of their activities at that instant.

The time interval in which the number of radioactive nuclei reduced / disintegrated to half of initialvalue Let R1 and R2 be their activities thenR1=λ1N1R2=λ2N2R1R2=λ1N1λ2N2=N1T1N2T2=N1T2N2T1

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Define the term ‘Half-life’ of a radioactive substance. Two different radioactive substances have half-lives T₁ and T₂ and number of un decayed atoms at an instant, N₁ and N₂ , respectively. Find the ratio of their activities at that instant.

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Detailed Solution

The time interval in which the number of radioactive nuclei reduced / disintegrated to half of initial
value Let R₁and R₂ be their activities then
$\begin{array}{l} R_{1} = λ_{1} N_{1} \\ R_{2} = λ_{2} N_{2} \\ \frac{R_{1}}{R_{2}} = \frac{λ_{1} N_{1}}{λ_{2} N_{2}} = \frac{\frac{N_{1}}{T_{1}}}{\frac{N_{2}}{T_{2}}} = \frac{N_{1} T_{2}}{N_{2} T_{1}} \end{array}$