Editing Bohr model (section)

=== Haas atomic model<span class="anchor" id="Haas atomic model"></span> ===
In 1910, [[Arthur Erich Haas]] proposed a model of the hydrogen atom with an electron circulating on the surface of a sphere of positive charge. The model resembled Thomson's plum pudding model, but Haas added a radical new twist: he constrained the electron's potential energy, <math>E_\text{pot}</math>, on a sphere of radius {{mvar|a}} to equal the frequency, {{mvar|f}}, of the electron's orbit on the sphere times the [[Planck constant]]:<ref name=PaisInwardBound/>{{rp|197}}
<math display="block">E_\text{pot}= \frac{- e^2}{a} = hf </math>
where {{mvar|e}} represents the charge on the electron and the sphere.  Haas combined this constraint with the balance-of-forces equation. The attractive force between the electron and the sphere balances the [[centrifugal force]]:
<math display="block">\frac{e^2}{a^2} = ma(2\pi f)^2</math>
where {{mvar|m}} is the mass of the electron. This combination relates the radius of the sphere to the Planck constant:
<math display="block">a = \frac{h^2}{4\pi^2e^2m}</math>
Haas solved for the Planck constant using the then-current value for the radius of the hydrogen atom.
Three years later, Bohr would use similar equations with different interpretation. Bohr took the Planck constant as given value and used the equations to predict, {{mvar|a}}, the radius of the electron orbiting in the ground state of the hydrogen atom. This value is now called the [[Bohr radius]].<ref name=PaisInwardBound/>{{rp|197}}