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  • Activities of three radioactive substances and are represented by the curves 

Activities of three radioactive substancesA,B and C are represented by the curves A,B and C, in the figure. Then their half-lives T_{\frac{1}{2}}(A):T_{\frac{1}{2}}(B):T_{\frac{1}{2}}(C) are in the ratio :
 


Option: 1 2:1:1
Option: 2 3:2:1
Option: 3 2:1:3
Option: 4 4:3:1

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\begin{array}{l} \mathrm{R}=\mathrm{R}_{0} \mathrm{e}^{-\lambda \mathrm{t}} \\\\ \ln \mathrm{R}=\ln \mathrm{R}_{0}-\lambda \mathrm{t} \\\\ \lambda_{\mathrm{A}}=\frac{6}{10} \Rightarrow \mathrm{T}_{\mathrm{A}}=\frac{10}{6} \ln 2 \\\\ \lambda_{\mathrm{B}}=\frac{6}{5} \Rightarrow \mathrm{T}_{\mathrm{B}}=\frac{5 \ln 2}{6} \\\\ \lambda_{\mathrm{C}}=\frac{2}{5} \Rightarrow \mathrm{T}_{\mathrm{C}}=\frac{5 l \mathrm{n} 2}{2} \\\\ \frac{10}{6}: \frac{5}{6}: \frac{15}{6}:: 2: 1: 3 \end{array}

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Deependra Verma

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