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In the image, the Rydberg constant seems to have two units. How is that possible? enter image description here

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To convert between joules (units of energy) and inverse centimetres (conventional units of wavenumber) simply requires multiplication by a factor of $hc$. This is because

$$E = h\nu = \frac{hc}{\lambda} = hc\bar\nu$$

Of course, they are not literally equal, but they are physically equivalent.

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