If the difference between the (n+1)^{text{th} | vedclass

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(A) The Bohr radius for the $n^{	ext{th}}$ orbit is given by $r_n = r_0 n^2$,where $r_0$ is the radius of the first orbit.According to the problem,th

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$4$

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(A) The Bohr radius for the $n^{	ext{th}}$ orbit is given by $r_n = r_0 n^2$,where $r_0$ is the radius of the first orbit.According to the problem,the difference between the $(n+1)^{	ext{th}}$ and $n^{	ext{th}}$ Bohr radius is equal to the $(n-1)^{	ext{th}}$ Bohr radius:$r_{n+1} - r_n = r_{n-1}$Substituting the formula $r_n = r_0 n^2$:$r_0(n+1)^2 - r_0 n^2 = r_0(n-1)^2$Dividing both sides by $r_0$:$(n+1)^2 - n^2 = (n-1)^2$$(n^2 + 2n + 1) - n^2 = n^2 - 2n + 1$$2n + 1 = n^2 - 2n + 1$$n^2 - 4n = 0$$n(n - 4) = 0$Since $n$ must be a positive integer greater than $1$ for the $(n-1)^{	ext{th}}$ orbit to exist,we have $n = 4$.

If the difference between the $(n+1)^{\text{th}}$ Bohr radius and the $n^{\text{th}}$ Bohr radius is equal to the $(n-1)^{\text{th}}$ Bohr radius,then find the value of $n$.

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