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

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(A) The Bohr radius for the $n^{th}$ orbit is given by $r_n = a_0 n^2$, where $a_0$ is the Bohr radius constant.Given the condition: $r_{n+1} - r_n =

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$4$

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(A) The Bohr radius for the $n^{th}$ orbit is given by $r_n = a_0 n^2$, where $a_0$ is the Bohr radius constant.Given the condition: $r_{n+1} - r_n = r_{n-1}$.Substituting the formula: $a_0(n+1)^2 - a_0 n^2 = a_0(n-1)^2$.Dividing by $a_0$: $(n+1)^2 - n^2 = (n-1)^2$.Expanding the terms: $(n^2 + 2n + 1) - n^2 = n^2 - 2n + 1$.Simplifying: $2n + 1 = n^2 - 2n + 1$.Rearranging the equation: $n^2 - 4n = 0$.Factoring: $n(n - 4) = 0$.Since $n$ represents the orbit number, $n$ must be greater than $1$ for the $(n-1)^{th}$ orbit to exist. Thus, $n = 4$.

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

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