In my textbook (Chemistry Part - I for Class XI published by NCERT), there is an equation for the energy of an electron in an energy state: $$E_n = -R_\mathrm H\left(\frac{1}{n^2}\right)$$ and there is a paragraph below it with the following text:
where $R_\mathrm H$ is called Rydberg constant and its value is $2.18\times10^{-18}\ \text{J}$.
There is another section with the expression for the wavenumber ($\overline{\nu}$): $$\overline{\nu}=109\,677 \left(\frac{1}{n_1^2} - \frac{1}{n_2^2}\right)\ \text{cm}^{-1}$$ with a paragraph with the following text:
The value $109\,677 \space\text{cm}^{-1}$ is called the Rydberg constant for hydrogen.
I checked online and found that in most (all) websites (incl. Wikipedia), the value of Rydberg constant is $109\,677 \space\text{cm}^{-1}$. But when I searched for its value in joules, I found this website with the value of Rydberg constant $= 2.18\times10^{-18}\ \text{J}$.
How can Rydberg constant be written in joules?
Answer
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 $\pu{1 Ry} = Ry = hc \cdot R_\ce{H}$.
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