No two electrons can have the same 4 quantum numbers

[Sophia Henry]

Okay sorry last question about quantum numbers I think it is just the concept that I am having trouble the most with understanding conceptually.

Why can't two electrons have the same four quantum numbers? How on earth does every electron have a different set of quantum numbers? This doesn't make sense to me because I'm just basically absolutely positive that there isn't an unlimited amount of combinations of 4 numbers. Please help.

[alexia11]

To understand this concept, think of electrons within the scope of atomic orbitals and electron configurations. The quantum numbers describe the energy and size as well as orientation of an electron. When you are drawing out the electron configurations you cannot have electrons that are in the same orbital with the same spin. Meaning they differ in the magnetic quantum and spin magnetic quantum number. You cannot have an electron that is in the same orbital and has the same spin direction, therefore you need different quantum numbers to fulfill Hund’s Rule and Pauli exclusion principle. The other numbers refer to energy, size, and shape of an electron, which differ when looking at electron configurations.

[Miguel Hernandez LEC 3]

One way to think about this topic is to refer to the Pauli Exclusion Principle. This states that no two electrons can have the same 4 quantum numbers. Electrons in the same atom can share the first 3 quantum numbers however, the electrons must have different numbers for the final quantum number which determines electron spin. This principle is necessary because it prevents atoms from occupying the same space.