In the Franck-Hertz experiment, the first dip in the current-voltage graph for hydrogen is observed at $10.2 \, V$. The wavelength of light emitted by the hydrogen atom when excited to the first excitation level is $\qquad$ $nm$.
(Given $hc = 1245 \, eV \cdot nm$, $e = 1.6 \times 10^{-19} \, C$).

In Bohr's model of hydrogen-like species,which of the following is true?

In the Bohr model of a hydrogen-like atom,the force between the nucleus and the electron is modified as $F = \frac{e^2}{4\pi \varepsilon_0} \left( \frac{1}{r^2} + \frac{\beta}{r^3} \right)$,where $\beta$ is a constant. For this atom,the radius of the $n^{th}$ orbit in terms of the Bohr radius $\left( a_0 = \frac{\varepsilon_0 h^2}{m \pi e^2} \right)$ is:

When an electron in a hydrogen atom makes a transition from the $2^{nd}$ excited state to the ground state,it emits a photon of frequency $f$. The frequency of the photon emitted when an electron of $Li^{++}$ makes a transition from the $1^{st}$ excited state to the ground state is:

Explain the quantization of angular momentum by considering the electron as a wave in an atom.

Using Bohr's model, calculate the ratio of the magnetic fields generated due to the motion of the electrons in the $2^{nd}$ and $4^{th}$ orbits of hydrogen atom. (in $32$ : $1$)