Particles have a characteristic wavelength such that
Q = particle momentum W = particle wavelength h = Planck's constant = 6.62*10^-34 Joule seconds Q W = h de Broglie formulaSuppose an electron orbits a proton (a hydrogen atom). According to the Bohr theory, the number of wavelengths experienced by the electron during one orbit is an integer.
R = Orbit radius C = Orbit circumferenceThe Bohr assumption:
C = N W where N is an integer N = 1 corresponds to the S orbital N = 2 corresponds to the P orbital N = 3 corresponds to the D orbital M = Electron mass = 9.11*10^-31 kg V = Electron velocity Q = Electron momentum = M V e = Electron charge = -1.60*10^-19 Coulombs p = Proton charge = +1.60*10^-19 Coulombs k = Coulomb constant = 9.0*10^9 Newtons meters^2 / Coulombs^2 Fe= Electric force = k p e / R^2 Fc= Centripetal force = M V^2 / RFor an electron in a circular orbit,
Fe = FcThis sets the characteristic size of the hydrogen atom.
E = Electric potential energy = k p e / R = Energy required to steal the electron from the proton (the "ionization energy").