The wavelength of the first Balmer line caused by a transition from the $n=3$ level to the $n=2$ level in hydrogen is $\lambda_1$. The wavelength of the line caused by an electronic transition from $n=5$ to $n=3$ is

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

The energy of $He^{+}$ ion in its first excited state is $......eV$ (The ground state energy for the Hydrogen atom is $-13.6\,eV$).

An electron in a hydrogen atom,after absorbing energy photons,can jump between energy states $n_1$ and $n_2$ $(n_2 > n_1)$. It then returns to the ground state,emitting six different wavelengths in the emission spectrum. The energy of the emitted photons can be equal to,less than,or greater than the absorbed photon energy. Determine $n_1$ and $n_2$.

The radius of the first orbit of a hydrogen atom is $0.5 \, \mathring{A}$ and the speed of the electron is $2.2 \times 10^6 \, m/s$. Find the magnetic induction at the proton due to the motion of the electron in $Tesla$.

The electron in a hydrogen atom makes a transition from the $M$ shell to the $L$ shell. The ratio of the magnitudes of the initial to the final centripetal acceleration of the electron is: