The ratio of areas within the electron orbits for the first excited state to the ground state for a hydrogen atom is (in $ : 1$)

Hydrogen $(_1H^1)$,Deuterium $(_1H^2)$,singly ionized Helium $(_2He^4)^+$,and doubly ionized Lithium $(_3^6Li)^{++}$ all have one electron around the nucleus. Consider an electron transition from $n = 2$ to $n = 1$. If the wavelengths of emitted radiation are $\lambda_1, \lambda_2, \lambda_3$,and $\lambda_4$ respectively,then approximately which one of the following is correct?

In the Bohr model,an electron of mass $m$ moves in a circular orbit around the proton. Considering the orbiting electron as a circular current loop,find the magnetic moment of the hydrogen atom when the electron is in the $n$th orbit. (Assume $h$ is Planck's constant)

If the atom $_{100}Fm^{257}$ follows the Bohr model and the radius of the outermost shell of $_{100}Fm^{257}$ is $n$ times the Bohr radius,then find $n$.

Considering the Bohr model of hydrogen-like atoms,the ratio of the radius of the $5^{\text{th}}$ orbit of the electron in $Li^{2+}$ to that in $He^{+}$ is:

The ratio of the kinetic energy to the total energy of an electron in a Bohr orbit is