Find the energy levels of the hydrogen atom by following
Bohr’s derivation. Bohr assumed in 1913 that the electron goes around the proton in a
circular orbit with angular momentum L having quantized values L = n?, where n = 1, 2,
3, … This equation plus F = ma (where F is the electrical attractive force between the
proton and electron) are two equations for the two unknowns, the radius r and velocity v.
(Note that this is a highly simplified treatment, which however does give the correct
quantum mechanical energies. Note also that the “fine structure constant” ? is defined in
terms of fundamental constants as ? ? e2/(4??0?c) and has the numerical value
? = 1/137.036 .)
The light emitted by the hydrogen atom’s transition from the n =
3 to the
n = 2 energy level is called H?.
(a) Find the energy E of the photons of this light in eV.
(b) Find the frequency ? of this light by using Planck’s formula E = h?.
(c) Find the wavelength ?. What is the color of this light?