What is the unit of the Rydberg Constant? In the image, the Rydberg constant seems to have two units. How is that possible?
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.