# Where do the four atomic quantum numbers come from?

Feb 20, 2017

See below.

#### Explanation:

Niels Bohr in 1913 was the first person to introduce a quantum number.

The Bohr model used only a single quantum number $n$ to specify the energy levels and hence the size of the two-dimensional orbits in which the electrons traveled.

In 1925, Erwin Schrödinger developed his three-dimensional quantum mechanical model of the atom.

He introduced three quantum numbers:

• $n$, the principal quantum number, which specified the energy and size of the orbital.
• $l$, the azimuthal quantum number, which specified the shape of the orbital
• ${m}_{l}$, the magnetic quantum number, which specified the orientation of the orbital in a magnetic field.

Also in 1925, George Uhlenbeck and Samuel Goudsmit introduced a fourth quantum number, called the spin quantum number $s$ of an electron.

And that’s where our four quantum numbers come from.