Magnetic field at the centre of a hydrogen-like atom (atomic number $= Z$) due to the motion of an electron in the $n^{th}$ orbit is proportional to

$A$ small particle of mass $m$ moves in such a way that its potential energy $U = \frac{1}{2} m \omega^2 r^2$,where $\omega$ is a constant and $r$ is the distance of the particle from the origin. Assuming Bohr's quantization of angular momentum and a circular orbit,the radius of the $n^{\text{th}}$ orbit will be proportional to:

The gyromagnetic ratio of an electron in a hydrogen atom,according to the Bohr model,is

Consider two different hydrogen atoms. The electron in each atom is in an excited state. Is it possible for the electrons to have different energies but the same orbital angular momentum according to the Bohr model?

The ionization energy of hydrogen is $13.6 \, eV$. If $h = 6.6 \times 10^{-34} \, J \cdot s$,the order of magnitude of the Rydberg constant $R$ will be:

$A$ hydrogen atom in its ground state absorbs $10.2 \; eV$ of energy. The angular momentum of the electron of the hydrogen atom will increase by the value of ............... $\times 10^{-34} \; J \cdot s$ (Given,Planck's constant $h = 6.6 \times 10^{-34} \; J \cdot s$)