The ratio of centripetal acceleration for an electron revolving in the $3^{\text{rd}}$ orbit to the $5^{\text{th}}$ Bohr orbit of a hydrogen atom is:

Excitation energy of a hydrogen-like ion in its first excitation state is $40.8 \, eV$. Energy needed to remove the electron from the ion in the ground state is ........ $eV$.

The de-Broglie wavelength of the electron in the first Bohr orbit of the hydrogen atom is

Assuming the atom in the ground state,the expression for the magnetic field at a point (nucleus) in a hydrogen atom due to the circular motion of the electron is [$\mu_{0} =$ permeability of free space,$\epsilon_{0} =$ permittivity of free space,$m =$ mass of electron,$e =$ electronic charge,$h =$ Planck's constant].

In a Bohr atom,the total energy of an electron in the $n$-th allowed orbit is $E_n$ and its angular momentum is $J_n$. Then:

In a hydrogen-like atom with atomic number $Z$,an electron is in an excited state with principal quantum number $2n$. The maximum energy of a photon that can be emitted from this state is $204 \ eV$. If the electron transitions from the $2n$ orbit to the $n$ orbit,a photon with energy $40.8 \ eV$ is emitted. The value of $n$ is: