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The figure shows a graph between $\ln \left| {\frac{A_n}{A_1}} \right|$ and ln|n|, where A_n is the area enclosed by the n^th orbit in a hydrogen like atom. The correct curve is

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Detailed Solution

${A_n} = \pi r_n^2 \Rightarrow \frac{{{A_n}}}{{{A_1}}} = {\left( {\frac{{{r_n}}}{{{r_1}}}} \right)^2} = {\left( {\frac{n}{1}} \right)^4}\,\,\,\,\,\,\,\,\,\,\,\,(\because {r_n}\infty {n^2})$

Taking log on both the sides ${\log _e}\frac{{{A_n}}}{{{A_1}}} = 4\,{\log _e}(n)$

Comparing it with y = mx + c, graph (4) is correct

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