Pauli Exclusion Principle vs Hund Rule
After finding the atomic structure, there were so many models to describe how the electrons reside in an atom. Schrodinger came up with the idea of having “orbitals” in an atom. Pauli Exclusion Principle and Hund rule are also put forward to describe the orbitals and electrons in atoms.
Pauli Exclusion Principle
Pauli Exclusion Principle says that no two electrons in one atom can have all four quantum numbers as the same. Orbitals of an atom are described by three quantum numbers. These are principal quantum number (n), angular momentum/azimuthal quantum number (l) and magnetic quantum number (m_{l}). From these, principal quantum number defines a shell. It can take any integer value. This is similar to the period of the relevant atom in the periodic table. Angular momentum quantum number can have values from 0,1,2,3 to n1. The number of sub shells depends on this quantum number. And l determines the shape of the orbital. For example, if l=o then the orbital is s, and for p orbital, l=1, for d orbital l=2, and for f orbital l=3. Magnetic quantum number determines the number of orbitals of equivalent energy. In other words, we call these degenerate orbitals. m_{l }can have values from –l to +l. Other than these three quantum numbers there is another quantum number which defines the electrons. This is known as electrons spin quantum number (m_{s}) and has the values +1/2 and 1/2. So, to specify the state of an electron in an atom we need to specify all four quantum numbers. Electrons reside in atomic orbitals and only two electrons can live in an orbital. Further, these two electrons have opposite spins. Therefore, what is said in the Pauli Exclusion Principle is true. For example, we take two electrons in 3p level. The principle quantum number for both electrons is 3. l is 1 since the electrons are residing in a p orbital. m_{l} is 1,0 and +1. Therefore, there are 3 p degenerated orbitals. All these values are same for both electrons we are considering. But since the two electrons are residing in the same orbital they have opposite spins. Therefore, the spin quantum number is different (one has +1/2 and the other has 1/2).
Hund rule
Hund rule can be describes as follows.
“The most stable arrangement of electrons in the sub shells (degenerate orbitals) is the one with the greatest number of parallel spins. They have the maximum multiplicity. ”
According to this, each sub shell will fill with an electron in parallel spin before it is doubly filled with another electron. Because of this filling pattern, electrons are less shielded from the nucleus; thus, they have the highest electron nuclear interactions.
What is the difference between Pauli Exclusion Principle and Hund Rule? • Pauli Exclusion Principle is about quantum numbers of an atom. Hund rule is about how electrons are filled to the orbitals of an atom. • Pauli Exclusion Principle says of having only two electrons per orbital. And Hund rule says that only after filling one electron to each orbital, electron pairing will happen. • Pauli Exclusion Principle describes how electrons in the same orbitals have opposite spins. This can be can be used to explain the Hund rule.

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