Final answer:
Quantum numbers are used to describe the state of an electron in an atom and include the principal, azimuthal, magnetic, and spin quantum numbers. Each quantum number has specific rules that must be followed for the set to be valid. The Pauli exclusion principle further restricts the possible combinations of quantum numbers for electrons in the same orbital.
Step-by-step explanation:
The validity of quantum numbers for an electron in an atom is foundational to understanding the substructure of matter and the behavior of electrons. There are four quantum numbers used to describe the state of an electron in an atom: n (principal quantum number), l (azimuthal or angular momentum quantum number), ml (magnetic quantum number), and ms (spin quantum number).
The first quantum number, n, indicates the energy level and can be any positive integer starting from 1. The second quantum number, l, is related to the shape of the orbital and can take on any integer value from 0 to n-1. The third quantum number, ml, corresponds to the orientation of the orbital in space and can range from -l to +l, including zero. Finally, the fourth quantum number, ms, describes the intrinsic spin of the electron and can be +1/2 or -1/2, representing spin-up or spin-down, respectively.
According to the Pauli exclusion principle, no two electrons in the same atom can have the same set of all four quantum numbers. This principle limits the occupancy of each orbital to two electrons, which must have opposite spins.
When evaluating the validity of a set of quantum numbers, it is important to check if they respect these rules. For example, the set (n = 1, l = 0, m = 0, ms = +1/2) is valid because it satisfies the conditions for each quantum number and follows the exclusion principle.