Calculate

(i) the radius of the second orbit of hydrogen atom, and

(ii) total energy of electron moving in the second orbit.

The ground state energy of hydrogen atom is $-13.6 \mathrm{eV}.$ If an electron makes a transition from an energy level $-0.85 \mathrm{eV}$ to $-1.51 \mathrm{eV},$ calculate the wavelength of the spectral line emitted. To which series of hydrogen spectrum does this wavelength belong?

The ground state energy of hydrogen atom is $-13.6 \mathrm{eV}$
(i) What are the potential energy and kinetic energy of an electron in the $3^{rd}$ excited state?
(ii) If the electron jumps to the ground state from the third excited state, calculate the frequency of photon emitted. Take, Rydberg's constant, $R = 1.1\times {10}^7 {\mathrm{m}}^{-1}$