The ratio of the speed of an electron in the ground state of the Bohr's first orbit of a hydrogen atom to the velocity of light in air is:

An electron in the hydrogen atom jumps from the first excited state to the ground state. What will be the percentage change in the speed of the electron (in $\%$)?

$A$ particular hydrogen-like ion emits radiation of frequency $2.92 \times 10^{15} \text{ Hz}$ when it makes a transition from $n=3$ to $n=1$. The frequency in $\text{Hz}$ of radiation emitted in the transition from $n=2$ to $n=1$ will be: (in $\times 10^{15}$)

In a hydrogen atom,find the magnetic field at the center in the ground state. Given that Bohr's radius is $r_{0} = 5 \times 10^{-11} \, m$ (in $T$).

Ionization potential of a hydrogen atom is $13.6 \text{ eV}$. Hydrogen atoms in the ground state are excited by monochromatic radiation of photon energy $12.1 \text{ eV}$. According to Bohr's theory,the number of spectral lines emitted by the hydrogen atoms will be:

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.