Bohr model and hydrogen spectrum

If one were to apply Bohr model to a particle of mass 'm' and charge 'q' moving in a plane under the influence of a magnetic field 'B', the energy of the charged particle in the n$^{\text{th}}$ level will be :

The de - Broglie wavelength associated with the electron in the n = 4 level is :

The radiation corresponding to $3\to2$ transition of hydrogen atom falls on a metal surface to produce photoelectrons. These electrons are made to enter a magnetic field of $3\times10^{-4}$ T. If the radius of the largest circular path followed by these electrons is 10.0 mm, the work function of the metal is close to :

Hydrogen $\left({}_1\mathrm H^1\right)$, Deuterium $\left({}_1\mathrm H^2\right)$, singly ionised Helium $\left({}_2\mathrm{He}^4\right)^+$ and doubly ionised lithium $\left({}_3\mathrm{Li}^6\right)^{++}$ all have one electron around the nucleus. Consider an electron transition from $n=2$ to $n=1$. If the wave lengths of emitted radiation are $\lambda_1$, $\lambda_2$, $\lambda_3$ and $\lambda_4$ respectively then approximately which one of the following is correct ?

If the binding energy of the electron in a hydrogen atom is 13.6 eV, the energy required to remove the electron from the first excited state of $\ce{Li^{++}}$ is :

The radius of the orbit of an electron in a Hydrogen-like atom is $4.5a_0$, where $a_0$ is the Bohr radius. Its orbital angular momentum is $\dfrac{3h}{2\pi}$. It is given that $h$ is Planck constant and $R$ is Rydberg constant. The possible wavelength(s), when the atom de-excites, is (are)

The wavelength of the first spectral line in the Balmer series of hydrogen atom is 6561 Å. The wavelength of the second spectral line in the Balmer series of singly-ionized helium atom is

A diatomic molecule has moment of inertia $I$. By Bohr's quantization condition its rotational energy in the $n^{\text{th}}$ level ($n=0$ is not allowed) is

It is found that the excitation frequency from ground to the first excited state of rotation for the CO molecule is close to $\dfrac4\pi\times10^{11}$ Hz. Then the moment of inertia of CO molecule about its center of mass is close to (Take $h=2\pi\times10^{-34}$ J s)

The quantum number $n$ of the state finally populated in He⁺ ions is

The wavelength of light emitted in the visible region by He⁺ ions after collisions with H atoms is

The ratio of the kinetic energy of the $n=2$ electron for the H atom to that of He⁺ ion is

The largest wavelength in the ultraviolet region of the hydrogen spectrum is 122 nm. The smallest wavelength in the infrared region of the hydrogen spectrum (to the nearest integer) is