In a hydrogen atom,if r_n is the radius of th | vedclass

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(B) According to Bohr's postulate for the quantization of angular momentum,the orbital angular momentum $L_n$ of an electron in the $n^{th}$ orbit is

Vedclass · Accepted Answer

$L_n \propto \sqrt{r_n}$

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(B) According to Bohr's postulate for the quantization of angular momentum,the orbital angular momentum $L_n$ of an electron in the $n^{th}$ orbit is given by $L_n = \frac{nh}{2\pi}$.Thus,$L_n \propto n$.The radius of the $n^{th}$ orbit in a hydrogen atom is given by $r_n = \frac{n^2 h^2 \epsilon_0}{\pi m e^2}$.Thus,$r_n \propto n^2$,which implies $n \propto \sqrt{r_n}$.Substituting $n \propto \sqrt{r_n}$ into the relation $L_n \propto n$,we get $L_n \propto \sqrt{r_n}$.

In a hydrogen atom,if $r_n$ is the radius of the $n^{th}$ orbit and $L_n$ is the orbital angular momentum,then which of the following relations is correct?

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