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

Question

Dr. Abubacker · Accepted Answer

(a) $A_{n} = \pi r_{n}^{2} \Rightarrow \frac{A_{n}}{A_{1}} = \left( \frac{r_{n}}{r_{1}} \right)^{2} = \left( \frac{n}{1} \right)^{4}\ \ \lbrack\because r_{n} \propto n^{2}\rbrack$
Taking $l{og}_{e}$ 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

Q. 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

Explanation

Reviewed by Dr. Abubacker

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