What is Quantum numbers?

The state of an electron in an atom is labelled by four numbers:

• the principal quantum number $n = 1, 2, 3, \dots$, which mainly fixes the energy and the size;
• the azimuthal quantum number (or secondary quantum number) $l = 0, 1, \dots, n-1$, which fixes the shape; $l = 0, 1, 2, 3$ are written s, p, d, f;
• the magnetic quantum number $m_l = -l, -l+1, \dots, l$, which fixes the orientation ($2l + 1$ values);
• the spin quantum number $m_s = +\tfrac12$ or $-\tfrac12$, an intrinsic property of the electron, drawn as an arrow up or down.