The expression for Bohr's radius of an atom i | vedclass

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(A) According to Bohr's theory,the radius of the $n^{th}$ orbit of a hydrogen-like atom is given by the formula: $r_n = \frac{n^2 h^2}{4 \pi^2 m k Z e

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$r = \frac{n^2 h^2}{4 \pi^2 m e^2 Z}$

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(A) According to Bohr's theory,the radius of the $n^{th}$ orbit of a hydrogen-like atom is given by the formula: $r_n = \frac{n^2 h^2}{4 \pi^2 m k Z e^2}$.Assuming the constant $k = \frac{1}{4 \pi \epsilon_0}$,the expression simplifies to $r = \frac{n^2 h^2 \epsilon_0}{\pi m Z e^2}$.However,in the given options,the standard representation for the radius of the $n^{th}$ orbit is $r = \frac{n^2 h^2}{4 \pi^2 m Z e^2}$ (where $k$ is implicitly included or units are in $CGS$). Thus,option $A$ and $B$ represent the correct physical relationship.

The expression for Bohr's radius of an atom is

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