Let A_n be the area enclosed by the n^{th} or | vedclass

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(D) The radius of the $n^{th}$ orbit of a hydrogen atom is given by $r_n = n^2 a_0$.The area of the $n^{th}$ orbit is given by $A_n = \pi r_n^2 = \pi

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both $(A)$ and $(B)$

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(D) The radius of the $n^{th}$ orbit of a hydrogen atom is given by $r_n = n^2 a_0$.The area of the $n^{th}$ orbit is given by $A_n = \pi r_n^2 = \pi (n^2 a_0)^2 = \pi n^4 a_0^2$.For the first orbit $(n=1)$,the area is $A_1 = \pi a_0^2$.Taking the ratio,we get $\frac{A_n}{A_1} = \frac{\pi n^4 a_0^2}{\pi a_0^2} = n^4$.Taking the natural logarithm on both sides,we get $\ln \left( \frac{A_n}{A_1} \right) = \ln (n^4) = 4 \ln (n)$.Comparing this with the equation of a straight line $y = mx + c$,where $y = \ln (A_n/A_1)$,$x = \ln (n)$,$m = 4$,and $c = 0$,we conclude that the graph is a straight line passing through the origin with a slope of $4$.

Let $A_n$ be the area enclosed by the $n^{th}$ orbit in a hydrogen atom. The graph of $\ln (A_n/A_1)$ against $\ln (n)$:

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