JEE Mains · Physics · STD 12 - Nuclei
- JEE Mains 2021
- Hard
- MCQ
Two radioactive substances \(X\) and \(Y\) originally have \(N _{1}\) and \(N _{2}\) nuclei respectively. Half life of \(X\) is half of the half life of \(Y\). After three half lives of \(Y\), number of nuclei of both are equal. The ratio \(\frac{ N _{1}}{ N _{2}}\) will be equal to
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Answer & Solution
Correct Answer
(C) \(\frac{8}{1}\)
Step-by-step Solution
Detailed explanation
\(T _{ x }= t ; T _{ y }=2 t\)
\(3 T _{ y }=6 t\)
\(N _{1}^{\prime}= N _{2}^{\prime}\)
\(N _{1} e ^{-\lambda_{1} 6 t }= N _{2} e ^{-\lambda_{2} 6 t }\)
\(\frac{ N _{1}}{ N _{2}}= e ^{\left(\lambda_{1}-\lambda_{2}\right) 6 t }= e ^{\ln 2\left(\frac{1}{t}-\frac{1}{2 t }\right) \times 6 t }= e ^{(1 n 2) \times 3}= e ^{ ln 8}=8\)
\(\frac{ N _{1}}{ N _{2}}=\frac{8}{1}\)
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