Chemistry - Can Rydberg constant be in joules?

Solution 1:

Authors may be sloppy about notation in this matter. I recommend considering $R_\ce{H} \approx \pu{10973 cm-1}$ and $Ry \approx \pu{2.18e-18 J}$, noting $Ry = hc \cdot R_\ce{H}$. Units of wavenumbers $(\pu{cm-1})$ and energy are often considered interchangeable in practice because they are proportional to each other by the constant value $hc$.

In my notes, I would always be sure to write $R_\ce{H}$ or $Ry$ to explicitly remind myself "which" Rydberg constant I was using (in fact I merged the R and y into a single symbol because I didn't like the suggestion of multiplication.)

Note also that there is a unit of energy known as a Rydberg, with $\pu{1 Ry} = Ry = hc \cdot R_\ce{H}$.

Solution 2:

Rydberg constant $R_∞$ is usually given in reciprocal length units historically and because it's determined from hydrogen and deuterium transition frequencies [1]. Current value (in $\pu{m-1}$) is listed at NIST [2] website (accessed 2019-06-05):

$$R_∞ = \pu{10973731.568160(21) m-1}$$

Since it's an energy unit, one can convert it to SI rather trivially via multiplying the value in reciprocal length units by $hc$ ($h$ is the Planck constant; $c$ is the speed of light in vacuum):

$$E = hν = \frac{hc}{λ} \quad\text{or}\quad R_∞[\pu{J}] = hc\cdot R_∞[\pu{m-1}]$$

resulting in the following value:

$$R_∞ = \pu{2.1798723611035(42)e-18 J}$$


  1. Mohr, P. J.; Newell, D. B.; Taylor, B. N. CODATA Recommended Values of the Fundamental Physical Constants: 2014. Reviews of Modern Physics 2016, 88 (3).
  2. Tiesinga E.; Mohr P. J.; Newell D. B.; Taylor, B. N. "The 2018 CODATA Recommended Values of the Fundamental Physical Constants" (Web Version 8.0). Database developed by J. Baker, M. Douma, and S. Kotochigova. Available at, National Institute of Standards and Technology, Gaithersburg, MD 20899. 2019.

Solution 3:

In spectroscopy and related fields it is common to measure energy levels in units of reciprocal centimeters (e.g., IR and Raman spectroscopy). Strictly speaking, these units ($\pu{cm^{−1}}$) are not energy units, but units proportional to energies, with $hc$ being the proportionality constant (Wikipedia). In general, $hc$ can be attributed to the value $\pu{1.986E-23 J cm}$. Hence: $$R_∞ = \pu{109677 cm^{−1}}$$

$$\pu{1 Ry} = \pu{109677 cm^{−1}} \times hc = \pu{109677 cm^{−1}} \times \pu{1.986E-23 J cm} = \pu{2.178E-18 J}$$