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Q. In Bohr theory of hydrogen atom, let $r, v$ and $E$ be the radius of orbit, speed of electron and the total energy of the electron respectively. Which of the following quantities is proportional to the quantum number $n ?$

Atoms

Solution:

According to Bohr theory of hydrogen atom, $r \propto n^{2}$
$v \propto \frac{1}{n}$
$E \propto \frac{1}{n^{2}} $
$ \therefore v r \propto n$