Quantum Number Rules

Quantum numbers can be thought of as labels for an electron. Every electron in an atom has a unique set of four quantum numbers.

The principal quantum number n corresponds to the shell in which the electron is located. Thus n can therefore be any integer. For example, an electron in the 2p subshell has a principal quantum number of n=2 because 2p is in the second shell.

The azimuthal or angular momentum quantum number ℓ corresponds to the subshell in which the electron is located. s subshells are coded as 0, p subshells as 1, d as 2, and f as 3. For example, an electron in the 2p subshell has ℓ=1. As a rule, ℓ can have integer values ranging from 0 to n−1.

The magnetic quantum number mℓcorresponds to the orbital in which the electron is located. Instead of 2px, 2py, and 2pz, the three 2p orbitals can be labeled −1, 0, and 1, but not necessarily respectively. As a rule, mℓcan have integer values ranging from −ℓ to +ℓ.

The spin quantum number ms corresponds to the spin of the electron in the orbital.  A value of 1/2 means an “up” spin, whereas −1/2means a “down” spin.

What is the only possible value of mℓ for an electron in an orbital?

What are the possible values of mℓ for an electron in a d orbital?