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Quantum Number

Given rn+1-...

Question

Given $r_{n + 1} - r_{n - 1} = 2 r_{n}$ , where $r_{n}, r_{n - 1}, r_{n + 1}$ are Bohr radius for hydrogen atom in $n^{t h}, (n - 1)^{t h}, (n + 1)^{t h}$ shells respectively. The value of $n$ is:

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Solution

As radius of electron is-
$r \propto \frac{n^{2}}{Z}$
$r_{n + 1} - r_{n - 1} = 2 r_{n}$
$(n + 1)^{2} - (n - 1)^{2} = 2 n^{2}$
$4 n = 2 n^{2}$
$∴ n = 2$

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