Question

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

Answer 1

$E=-13.6[\frac{1}{{n_f}^2}-\frac{1}{{n_i}^2}]$

$E=-13.6[\frac{1}{3^2}-\frac{1}{4^2}]$

$E=0.6611eV$

$\lambda =\frac{hc}{E}$

$=\frac{1240eV-nm}{0.6611nm}$

$=1876nm$

This wavelength belongs to the Paschen series of Hydrogen spectrum.