In terms of Bohr radius $a_0$,the radius of the second Bohr orbit of a hydrogen atom is given by

Using the formula for the radius of the $n^{th}$ orbit $r_n = \frac{n^2 h^2 \epsilon_0}{\pi m Z e^2}$,derive an expression for the total energy of an electron in the $n^{th}$ Bohr orbit.

Radius of the second Bohr orbit of a singly ionized helium atom is ......... $ \mathring A $

An electron in an excited state of $Li^{2+}$ ion has angular momentum $\frac{3 h}{2 \pi}$. The de-Broglie wavelength of the electron in this state is $p \pi a_{0}$ (where, $a_{0} = \text{Bohr radius}$). The value of $p$ is

The total energy of an electron in the $n^{th}$ orbit of a hydrogen atom is $E_n$. The total energy of an electron in the $n^{th}$ orbit of a $He^+$ ion is .........

In a hydrogen atom,an electron transitions from an orbit of radius $R$ to an orbit of radius $4R$. What is the ratio of their time periods?