Editing Quantum Hall effect (section)

== Bohr atom interpretation of the von Klitzing constant ==

The value of the von Klitzing constant may be obtained already on the level of a single atom within the [[Bohr model]] while looking at it as a single-electron Hall effect. While during the [[cyclotron|cyclotron motion]] on a circular orbit the centrifugal force is balanced by the [[Lorentz force]] responsible for the transverse induced voltage and the Hall effect, one may look at the Coulomb potential difference in the Bohr atom as the induced single atom Hall voltage and the periodic electron motion on a circle as a Hall current. Defining the single atom Hall current as a rate a single electron charge <math>e</math> is making Kepler revolutions with angular frequency <math>\omega</math>
: <math>I = \frac{\omega e}{2\pi},</math>
and the induced Hall voltage as a difference between the hydrogen nucleus Coulomb potential at the electron orbital point and at infinity:
: <math>U=V_\text{C}(\infty) - V_\text{C}(r) = 0 - V_\text{C}(r) = \frac{e}{4\pi\epsilon_0 r}</math>

One obtains the quantization of the defined Bohr orbit Hall resistance in steps of the von Klitzing constant as
: <math>R_\text{Bohr}(n) = \frac{U}{I} = n\frac{h}{e^2}</math>
which for the Bohr atom is linear but not inverse in the integer ''n''.