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? I read while I was studying that electrons can't have the same four quantum numbers. How on earth does every electron have a different set of quantum numbers? That is my question. This doesn't make sense to me because wouldn't there have to be an unlimited amount of combinations of 4 numbers but wouldn't that not be possible? I understand what the quantum numbers represent and how they show the shell subshell and orientation and spin of electrons. I just don't understand this that electrons all have unique electron configurations?!

[Daniel P 3J]

While there are indeed many possible combinations of quantum numbers, the Pauli Exclusion Principle ensures that no two electrons in the same atom can have the same set of quantum numbers. This principle is essential for understanding the stability and behavior of electrons in atoms, as well as the structure of the periodic table.

[Valeria Perez 3J]

Every electron cannot have the same four quantum numbers because at the very least, if they are in the exact same orbital, they cannot be rotating in the same direction , therefore they will have at least one different quantum number. (The quantum number I am referring to is m_s, which can have a value of +1/2 or -1/2)

[Amber Gimino 1F]

The 4 quantum numbers are the principle quantum number (n), the angular momentum quantum number (l), the magnetic quantum number (ml), and the spin magnetic quantum number (ms). These 4 quantum numbers essentially give the "address" of an electron and, in a given atom, no two electrons can have the same four quantum numbers. According to the Pauli exclusion principle, each orbital in an atom can only hold two electrons, each with opposite spin. We know that, depending on the atom, there can be 1 s-orbital, 3 p-orbitals, 5 d-orbitals, and 7 f-orbitals, and within each orbital there can only be two electrons (one electron that spins in the counterclockwise direction and one electron that spins in the clockwise direction) due to electron repulsion. For example, in an atom with a filled px-orbital, the px-orbital will contain one electron with a counterclockwise rotation (ms=1/2) and one electron with a clockwise rotation (ms=-1/2). Although these two electrons can have the same n, l, and ml, they differ in the value of the 4th quantum number, ms. Therefore, no two electrons in the same orbital can have the same 4 quantum numbers, but they can have up to three of the same quantum numbers.