If $\lambda_1$ and $\lambda_2$ denote the wavelengths of de Broglie waves for electrons in the first and second Bohr orbits in a hydrogen atom,then $\lambda_1/\lambda_2$ is equal to

Consider a hydrogen-like atom whose energy in the $n^{th}$ excited state is given by $E_n = - \frac{13.6 Z^2}{n^2}$. When this excited atom makes a transition from an excited state to the ground state, the most energetic photons have energy $E_{max} = 52.224 \ eV$ and the least energetic photons have energy $E_{min} = 1.224 \ eV$. The atomic number of the atom is:

Find the radius of $Be^{3+}$ ions in its ground state assuming Bohr's model to be valid $(a_0 = 53 \ pm)$. (in $pm$)

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:

In the Auger process,an atom makes a transition to a lower state without emitting a photon. The excess energy is transferred to an outer electron which may be ejected by the atom. (This is called an Auger electron). Assuming the nucleus to be massive,calculate the kinetic energy of an $n = 4$ Auger electron emitted by Chromium by absorbing the energy from an $n = 2$ to $n = 1$ transition.

Using the Bohr model,calculate the electric current created by the electron when the $H$-atom is in the ground state.