If E and L denote the magnitudes of total ene | vedclass

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(A) According to Bohr's theory,the total energy $E$ of an electron in the $n^{	ext{th}}$ orbit is given by $E = -\frac{13.6 Z^2}{n^2} 	ext{ eV}$,whi

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$L \propto \frac{1}{\sqrt{E}}$

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(A) According to Bohr's theory,the total energy $E$ of an electron in the $n^{	ext{th}}$ orbit is given by $E = -\frac{13.6 Z^2}{n^2} 	ext{ eV}$,which implies $E \propto \frac{1}{n^2}$.The angular momentum $L$ of an electron in the $n^{	ext{th}}$ orbit is given by $L = \frac{nh}{2\pi}$,which implies $L \propto n$.From the relation $L \propto n$,we have $n \propto L$.Substituting this into the energy relation: $E \propto \frac{1}{n^2} \implies E \propto \frac{1}{L^2}$.Taking the square root of both sides,we get $\sqrt{E} \propto \frac{1}{L}$,which rearranges to $L \propto \frac{1}{\sqrt{E}}$.

If $E$ and $L$ denote the magnitudes of total energy and of angular momentum of an electron in a Bohr orbit,then the true relation between them is:

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