Atomic Structure – Quantum Numbers Identify the principle stated by the rule: ‘‘No two electrons in an atom can have the same set of four quantum numbers.’’

Introduction / Context:
Quantum numbers (n, l, m_l, m_s) uniquely describe the state of an electron in an atom. This question targets a foundational postulate that governs electron occupancy of orbitals and explains the structure of the periodic table and electron configurations.

Given Data / Assumptions:

• Statement: No two electrons in an atom can share all four quantum numbers.
• Four quantum numbers: principal n, azimuthal l, magnetic m_l, and spin m_s.
• We must name the principle encapsulating the statement.

Concept / Approach:
The statement is the essence of Pauli’s exclusion principle. It restricts occupancy to at most two electrons per orbital with opposite spins (since n, l, m_l are the same for an orbital, m_s must differ). Aufbau principle is a filling order guideline (lowest energy first), while Newton’s and Bohr’s laws do not address quantum number uniqueness across electrons.

Step-by-Step Solution:

Verification / Alternative check:
Consider the 1s orbital: it holds two electrons only if spins are +1/2 and −1/2. A third electron cannot have a unique set of four quantum numbers in that orbital, so it must occupy a different state—exactly what Pauli’s principle dictates.

Why Other Options Are Wrong:

• Aufbau principle: Addresses order of filling, not uniqueness of quantum states.
• Bohr's law: Concerns energy levels and spectral lines, not fermion exclusion.
• Newton's law: Classical motion; not applicable to quantum electron states.

Common Pitfalls:
Confusing “how many can fit” (Pauli) with “which fills first” (Aufbau). Both are used together in configuration problems but answer different questions.

Final Answer:
Pauli's exclusion principle