The ratio of radii of $3^{\text{rd}}$ and $6^{\text{th}}$ Bohr's orbit in a hydrogen atom is

For an electron moving in the $n^{th}$ orbit of an $H$-atom,the angular velocity is proportional to:

In a hydrogen atom,the electron and proton are bound at a distance of about $0.53 \; \mathring{A}$.
$(a)$ Estimate the potential energy of the system in $eV$,taking the zero of the potential energy at infinite separation of the electron from the proton.
$(b)$ What is the minimum work required to free the electron,given that its kinetic energy in the orbit is half the magnitude of potential energy obtained in $(a)$?
$(c)$ What are the answers to $(a)$ and $(b)$ above if the zero of potential energy is taken at $1.06 \; \mathring{A}$ separation?

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

Monochromatic radiation is incident on a hydrogen $(H)$ sample which is in the ground state. If the hydrogen atoms emit radiation of $10$ different wavelengths after absorbing the incident radiation, then the wavelength of the incident radiation is (Let $hc = 1242 \text{ eV-nm}$) (in $\text{ nm}$)

In a hypothetical Bohr hydrogen atom, if the mass of the electron is doubled, then the energy of the electron in the first orbit is: (in $\text{ eV}$)