The difference between the radii of n^{text{t | vedclass

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(B) The radius of the $n^{	ext{th}}$ orbit of a hydrogen atom is given by $r_n = r_0 n^2$,where $r_0$ is the Bohr radius.Given the condition: $r_{n+1

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$\frac{2h}{\pi}$

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(B) The radius of the $n^{	ext{th}}$ orbit of a hydrogen atom is given by $r_n = r_0 n^2$,where $r_0$ is the Bohr radius.Given the condition: $r_{n+1} - r_n = r_{n-1}$.Substituting the formula: $r_0(n+1)^2 - r_0 n^2 = r_0(n-1)^2$.Dividing by $r_0$: $(n+1)^2 - n^2 = (n-1)^2$.Expanding the terms: $(n^2 + 2n + 1) - n^2 = n^2 - 2n + 1$.Simplifying: $2n + 1 = n^2 - 2n + 1$.Rearranging: $n^2 - 4n = 0$,which gives $n(n-4) = 0$.Since $n$ must be a positive integer,$n = 4$.The angular momentum $L$ of an electron in the $n^{	ext{th}}$ orbit is given by Bohr's quantization condition: $L = \frac{nh}{2\pi}$.Substituting $n = 4$: $L = \frac{4h}{2\pi} = \frac{2h}{\pi}$.

The difference between the radii of $n^{\text{th}}$ and $(n+1)^{\text{th}}$ orbits of a hydrogen atom is equal to the radius of the $(n-1)^{\text{th}}$ orbit of hydrogen. The angular momentum of the electron in the $n^{\text{th}}$ orbit is $.........$ ($h$ is Planck's constant).

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