Dimension of Rydberg Constant

Theorem
The Rydberg constant has the dimension $\mathsf {L^{-1} }$.

Proof
By definition, the Rydberg constant is:


 * $R_\infty = \dfrac {m_\E \E^4} {8 \varepsilon_0^2 h^3 c}$

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

We have: