The radius of the Bohr orbit in the ground state of a hydrogen atom is $0.5 \ \mathring{A}$. The radius of the orbit of the electron in the third excited state of $He^+$ will be ...... $\mathring{A}$.

When an electron is excited from its $4^{\text{th}}$ orbit to its $5^{\text{th}}$ stationary orbit,the change in the angular momentum of the electron is approximately (Planck's constant $= h = 6.63 \times 10^{-34} \text{ J s}$)

Show that the first few frequencies of light that is emitted when electrons fall to the $n^{\text{th}}$ level from levels higher than $n$,are approximate harmonics (i.e.,in the ratio $1:2:3...$) when $n >> 1$.

The energy required to ionise a hydrogen-like ion in its ground state is $9$ Rydbergs. What is the wavelength of the radiation emitted when the electron in this ion jumps from the second excited state to the ground state? ........$nm$

Consider an electron revolving in a circular orbit of a hydrogen atom,whose quantum number is $n=2$. The velocity of the electron in that orbit is

The product of linear momentum and angular momentum of an electron of the hydrogen atom is proportional to $n^{x}$,where $x$ is