First slide

Classical atomic models

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^th,(n-1)^th and (n+1)^th shell respectively. Calculate the value of n.

Moderate

Solution

$r_{n + 1} - r_{n - 1} = 2 r_{n}$
$0.529 \frac{{(n + 1)}^{2}}{Z} - 0.529 \frac{{(n - 1)}^{2}}{Z} = 2 \times 0.529 \frac{n^{2}}{Z}$
$n^{2} + 2 n + 1 - [n^{2} - 2 n + 1] = 2 n^{2}$
$4 n = 2 n^{2}$
n = 2

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