Final answer:
The statement is false; the Pauli exclusion principle dictates that no two electrons in an atom can have the same set of four quantum numbers, but it does allow an atomic orbital to contain two electrons with different spins.
Step-by-step explanation:
The statement is false. The Pauli exclusion principle states that no two electrons in an atom can have the exact same set of four quantum numbers, which are used to describe their properties within the atom.
According to the Pauli exclusion principle, an atomic orbital may indeed contain two electrons, but these electrons must have different spin quantum numbers. Each electron in an orbital is distinguished by its unique set of quantum numbers, and specifically, no two electrons can have the same spin quantum number when they are in the same orbital. This principle explains why certain electron configurations are allowed in atoms and others are not, limiting the number of electrons in atomic shells and subshells.