The principle which states that no two electrons in the same orbitals of an atom have same value for all four quantum numbers is the

1. Analyze the Question

The question asks for the specific scientific principle that dictates that electrons within an atom must have unique sets of quantum numbers. In other words, it describes the "rule" that prevents two electrons from being identical in their energy states and orientation.

2. Explain the Concept

To understand this, we look at the four quantum numbers that describe an electron:

• Principal quantum number ($n$): The energy level.
• Azimuthal quantum number ($l$): The shape of the orbital.
• Magnetic quantum number ($m_l$): The orientation in space.
• Spin quantum number ($m_s$): The direction of the electron's spin (+1/2 or -1/2).

The Pauli Exclusion Principle states that in a single atom, no two electrons can have the same set of all four quantum numbers. If two electrons occupy the same orbital (sharing the same $n, l,$ and $m_l$), they must have opposite spins ($m_s = +1/2$ and $-1/2$) to satisfy this principle.

3. Show the Solution

Let's evaluate the options provided:

• A. Aufbau principle: This states that electrons fill lower-energy orbitals before moving to higher-energy ones.
• B. Hund's rule: This states that electrons fill degenerate orbitals (orbitals with the same energy) singly first, with parallel spins, before pairing up.
• C. Pauli Exclusion principle: This is the correct principle that restricts the quantum numbers of electrons in an atom.
• D. Dilution principle: This is a concept in chemistry regarding the concentration of solutions, not atomic structure.

Since the question specifically describes the restriction on quantum numbers, the Pauli Exclusion Principle is the only correct answer.

4. Identify the Answer

The correct option is C.

5. Exam Tip

To remember these easily:

• Aufbau = "Building up" (filling from bottom to top).
• Hund's = "The Bus Rule" (people prefer to sit alone in a bus row before sharing a seat with a stranger).
• Pauli = "The ID Card Rule" (no two electrons can have the exact same "ID" or set of quantum numbers).