# Allowed energies for electrons in hydrogenic atoms

I have a question which may seem stupid, but I think I missing something here.

I see 2 equations describing allowed energies for electrons in hydrogenic atoms, being:
$$E = -\frac{hcRZ^2}{n^2}$$
And
$$E = -\frac{RZ^2}{n^2}$$
I assume that both are correct, but what makes the difference? Is it the same R for both of them? or the second R includes the h and c inside?
How would I tell the difference?

SpectraCat
I have a question which may seem stupid, but I think I missing something here.

I see 2 equations describing allowed energies for electrons in hydrogenic atoms, being:
$$E = -\frac{hcRZ^2}{n^2}$$
And
$$E = -\frac{RZ^2}{n^2}$$
I assume that both are correct, but what makes the difference? Is it the same R for both of them? or the second R includes the h and c inside?
How would I tell the difference?

They are trying to express the same relation, and you are correct that in the second version, the h and c have been "absorbed" into the R. In the first case the dimension of R is 1/length, and R comes from the Rydberg formula for the wavelength of a photon coupling two H-atom energy levels. In the second case, the dimension of R is energy, and the R stands for the Rydberg unit of energy, which is defined as the ground state energy of the H-atom in the approximation of infinite nuclear mass. The atomic unit of energy, the hartree, is exactly two Rydbergs.

Ok, thank you.
It's just that some textbooks use either one, and none explain the difference.

Now I understand!