Question

Two electrons in the same atomic orbital can be distinguished by their

• A. principal quantum number
• B. azimuthal quantum number
• C. magnetic quantum number
• D. spin quantum number

Answer 1

The Correct Option is D

In atomic physics, each electron in an atom is uniquely identified by a set of four quantum numbers: the principal quantum number (n), the azimuthal quantum number (l), the magnetic quantum number (m_l), and the spin quantum number (m_s). These quantum numbers describe the unique quantum state of an electron.

1. Principal Quantum Number (\(n\)): It defines the size and energy level of the atomic orbital. Electrons in the same orbital have the same \(n\).
2. Azimuthal Quantum Number (\(l\)): It describes the shape of the orbital. Electrons in the same orbital have the same \(l\).
3. Magnetic Quantum Number (\(m_l\)): It specifies the orientation of the orbital in space. Electrons in the same atomic orbital have the same \(m_l\).
4. Spin Quantum Number (\(m_s\)): This describes the spin of the electron. It can take one of two values: \(+\frac{1}{2}\) or \(-\frac{1}{2}\). This is the only quantum number that can differentiate between two electrons occupying the same orbital because they must have opposite spins (according to the Pauli Exclusion Principle).

Therefore, two electrons occupying the same atomic orbital are distinguished by their spin quantum number. This ensures they can still adhere to the Pauli Exclusion Principle, which states that no two electrons in the same atom can have identical sets of quantum numbers.