## Energy Levels of Non-Hydrogen Atoms

Just like for hydrogen, there is a formula for calculating the energy of electron transitions for ANY atom that only has one electron. This kind of thing happens more often on tests than in the real world. Example of atoms that this applies to are:

Since each of these atoms can only have one electron, each atom needs a progressively larger positive charge. Very quickly, the charges get ridiculously large.

Nonetheless, there are formulas to predict the energy and wavelength of electron transitions in these types of atoms:

Nonetheless, there are formulas to predict the energy and wavelength of electron transitions in these types of atoms:

Z is the atomic number of the atom (so it's 2 for Helium, 3 for Lithium, or 6 for Carbon). That's right.

**They're exactly the same as for hydrogen, except with an extra Z^2 term**. In fact, hydrogen follows this formula too, but since Z=1 we just simplify the formula.## Sample Question

Q: How much energy is RELEASED when an electron falls from n=6 to n=2 in a B(4+) atom? What wavelength is a photon with that amount of energy?

A: Notice how I used the same question as from the "Energy Levels of Hydrogen" page, but changed it to a B(4+) atom? This is solved the exact same way, just don't forget the Z^2!

E = 1.893 x 10^-18 J

wavelength = 1.05 x 10^-7 m = 105 nm

A: Notice how I used the same question as from the "Energy Levels of Hydrogen" page, but changed it to a B(4+) atom? This is solved the exact same way, just don't forget the Z^2!

E = 1.893 x 10^-18 J

wavelength = 1.05 x 10^-7 m = 105 nm