In a hydrogen atom,let $R$,$v$,and $E$ denote the radius,velocity,and total energy of the electron,respectively. Then,the principal quantum number $n$ is proportional to which of the following?

Given below are two statements $:$ one is labelled as Assertion $A$ and the other is labelled as Reason $R$.
Assertion $A :$ The Bohr model is applicable to hydrogen and hydrogen$-$like atoms only.
Reason $R :$ The formulation of Bohr model does not include repulsive force between electrons.
In the light of the above statements,choose the correct answer from the options given below $:$

According to Bohr's theory,the radius of an electron in an orbit described by principal quantum number $n$ and atomic number $Z$ is proportional to:

Given below are two statements.
Statement $(I) :$ The dimensions of Planck's constant and angular momentum are same.
Statement $(II) :$ In Bohr's model,electrons revolve around the nucleus only in those orbits for which angular momentum is an integral multiple of Planck's constant.
In the light of the above statements,choose the most appropriate answer from the options given below.

The ratio of the ionization energy of a Bohr's hydrogen atom to that of a Bohr's hydrogen-like lithium atom is:

The de-Broglie wavelength of an electron moving in the $n^{\text{th}}$ Bohr orbit of radius $r$ is