Question

Explain Pauli's exclusion principle with an example.

State and explain the following: (i) Aufbau principle (ii) Pauli exclusion principle. (iii) Hund's rule of maximum multiplicity.

Assertion: Each electron in an atom is described by a unique set of quantum numbers, defining its energy, shape, and spatial orientation. Reason: Quantum numbers are quantities that characterize the possible states of the system.

Due to the Pauli exclusion principle, two electrons cannot share the same set of quantum numbers within the same system; therefore, there is room for only two electrons in each spatial orbital. One of these electrons must have ms = +1/2, and the other must have ms = -1/2. Hund's first rule states that the lowest energy atomic state is the one that maximizes the total spin quantum number for the electrons in the open subshell. The orbitals of the subshell are each occupied singly with electrons of parallel spin before double occupation occurs. Two different physical explanations have been given for the increased stability of high multiplicity states. In the early days of quantum mechanics, it was proposed that electrons in different orbitals are further apart, so that electron–electron repulsion energy is reduced. However, accurate quantum-mechanical calculations (starting in the 1970s) have shown that the reason is that the electrons in singly occupied orbitals are less effectively screened or shielded from the nucleus, so that such orbitals contract and electron–nucleus attraction energy becomes greater in magnitude (or decreases algebraically).