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Q.
If in Bohr's atomic model, it is assumed that force between electron and proton varies inversely as $r^{4}$, energy of the system will be proportional to
Atoms
Solution:
$\frac{m v^2}{ r }=\frac{ k }{ r ^4} $
$V ^2=\frac{ k }{ mr ^3} $
$\text { we know } $
$mvr =\frac{ nh }{2 x } $
$m ^2 v ^2 r ^2=\frac{ n ^2 h ^2}{4 \pi^2} $
$\frac{ m ^2 kr }{ mr }=\frac{ n ^2 h ^2}{4 x ^2} $
$r =\frac{ mk ^3 \pi^2}{ n ^2 h ^2} $
$k \cdot f =\frac{1}{2} mv ^2=\frac{1}{2} m / \frac{ k }{ mr ^3} $
$=\frac{1}{2} m ^{ m } \frac{ K }{ m ^1 m ^3}$
$E \alpha n^6$