The MKS (meters, kilogram, secons) units system is the most frequently used. However, on the small length and energy scale of atoms this unit system is not very convenient. For example, the Rydberg constant is 2.18 x 10-18 Joules. Thus, energies are usually reported in other units. One common unit is the electron volt (eV). In this unit R = 13.6 eV. To convert to Joules we simply multiply the eV times the charge on an electron 1.602 x 10-19. Spectroscopists sometimes use eV, but the most common unit by far in spectroscopy is the cm-1. The reason for this may be that all of spectroscopy can be reported between 0.1 and 100,000 cm-1. Microwave (pure rotational spectra) range from 0.1 - 100 cm-1. Infrared (vibrational spectra range from 10 4,000 cm-1. Electronic spectra range from 1,000 - 100,000 cm-1. To convert from Joules to cm-1 we simply divide J by hc, where h is Planck's constant and c is the speed of light in cm/s. Note the use of cm in the speed of light. This is unusual since we would use meters for any other conversion in the MKS system. However, specifically in this case we need to cancel Joules and end up with cm-1. The units eV and cm-1 are proportional to energy, but they are really energy units. Nonetheless, we frequently refer to them as though the represented energy becuase of the proportionality. Note that 1 eV = 8065.5 cm-1. Finally, we note that we can define an atomic unit of energy, the Hartree. One Hartree = 27.2 eV or twice the value of the Rydberg constant
The natural unit of length that emerges from the semi-classical model for the hydrogen atom is the Bohr. We can use the symbol a0 for the Bohr. The Bohr is equal to 0.52977 Angstroms. The Bohr is the atomic unit of distance. In many calculations it is easiest convert to Bohrs. This is often done in computer codes as well since it simplifies the coding. At the end of the calculation it is easy to convert back to Angstroms.
