# Question #d6cb4

Dec 17, 2014

The Rydberg constant is a physical constant relating to atomic spectra and it represents the limiting value of the highest wavenumber (the inverse wavelength) of any photon that can be emitted from the hydrogen atom, or, alternatively, the wavenumber of the lowest-energy photon capable of ionizing the hydrogen atom from its ground state.

The value of the Rydberg constant is

${R}_{\infty} = \frac{{m}_{e} \cdot {e}^{4}}{m \cdot {\epsilon}_{0}^{2} \cdot {h}^{3} \cdot c} = 1.097373157 \cdot {10}^{7}$ per meter,

where we have

${m}_{e}$ - the rest mass of the electron
$e$ - elementary charge;
${\epsilon}_{0}$ - permittivity of free space;
$h$ - Planck's constant
$c$ - speed of light in a vacuum.

Rydberg's constant is based on the premise that the nucleus of the atom emitting light is exceedingly massive compared with a single orbiting electron (this is why the symbol for infinity, $\infty$, is used).

${R}_{\infty}$ appears in Rydebrg's formula for hydrogen

$\frac{1}{{\lambda}_{v a c}} = R \cdot \left(\frac{1}{n} _ {1}^{2} - \frac{1}{n} _ {2}^{2}\right)$, where

${\lambda}_{v a c}$ - the wavelenght of the EM radiation emitted in vacuum;
${n}_{1}$ and ${n}_{2}$ - the principal quantum numbers of the orbitals occupied before and after the 'quantum leap'.

Here's a video explaining Ryberg's formula in greater detail