Dimension of Bohr Radius

Theorem
The Bohr radius has the dimension $\mathsf L$.

Proof
By definition, the Bohr radius is:


 * $a_0 = \dfrac {\varepsilon_0 h^2} {\pi \E^2 m_\E}$

where:
 * $\varepsilon_0$ denotes the vacuum permittivity
 * $h$ denotes Planck's constant
 * $\E$ denotes the elementary charge
 * $m_\E$ denotes the electron rest mass

We have: