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

An electron is revolving in a circular orbit of radius $r$ in a hydrogen atom. The angular momentum of the electron is $L$. The relation between the magnetic dipole moment $(m)$ associated with it,the gyromagnetic ratio $(R)$,and $L$ is:

The wavelengths involved in the spectrum of deuterium $(_1^2D)$ are slightly different from that of hydrogen spectrum,because

In a system, a particle $A$ of mass $m$ and charge $-2q$ is moving in the nearest orbit around a very heavy particle $B$ having charge $+q$. Assuming Bohr's model of the atom to be applicable to this system, the orbital angular velocity of the particle $A$ is

The electrostatic potential energy of the electron in an orbit of hydrogen is $-6.8 \ eV$. The speed of the electron in this orbit is ($C$ is the speed of light in vacuum).

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