What is the aufbau principle and how does it determine electron configuration?

The aufbau principle states that electrons fill atomic orbitals from lowest to highest energy to achieve the lowest-energy configuration. This German term means "to build up." Electrons occupy the subshell of lowest energy available, subject to quantum number limitations. Each orbital can hold a maximum of two electrons before higher-energy subshells are filled.

Why do s orbitals sometimes have lower energy than d orbitals in higher shells?

Although energy generally increases with shell number, s orbitals penetrate closer to the nucleus than d orbitals. This greater penetration of s orbitals leads to the four-s orbital having lower energy than the three-d orbital, and the five-s orbital having lower energy than the four-d orbital, affecting the filling order.

What does Hund's rule of maximum multiplicity explain about electron filling?

Hund's rule states that electrons singly occupy all orbitals of a given energy level before pairing begins, and unpaired electrons must have parallel spins. This arrangement spreads electrons over a larger area, decreasing their shielding of each other and minimizing the atom's energy. For example, carbon's two 2p electrons occupy different orbitals with parallel spins.

What are degenerate orbitals and why does it matter for electron filling?

Degenerate orbitals are orbitals within the same subshell that have identical energy. Because they are equivalent in energy, an electron can enter any of the degenerate orbitals. This equivalence is why Hund's rule applies: electrons distribute among degenerate orbitals singly before pairing occurs, following the principle of maximum multiplicity.

How do you write the electron configuration for carbon using the aufbau principle?

Carbon has atomic number six. The 1s orbital fills first with two electrons, followed by the 2s orbital with two electrons. The fifth electron enters a 2p orbital, and the sixth electron enters a different 2p orbital with parallel spin, giving carbon the configuration 1s² 2s² 2p². This follows both the aufbau principle and Hund's rule.

What is the difference between core electrons and valence electrons?

Core electrons occupy inner shells and are not involved in bonding, while valence electrons occupy the outermost shell and participate in chemical reactions. For neon, two core electrons fill the inner shell and eight valence electrons fill the outermost shell to its maximum capacity, creating a stable noble gas configuration.

How does the Pauli exclusion principle relate to electron filling in orbitals?

The Pauli exclusion principle requires that electrons in the same orbital differ in their spin quantum number. When two electrons occupy one orbital, they must have opposite spins. This principle, combined with the aufbau principle and Hund's rule, ensures that each orbital accommodates a maximum of two electrons with opposite spins.

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The Aufbau Principle and Hund's Rule

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Recall that atomic orbitals have different energies and can accommodate two electrons each. The aufbau principle dictates the distribution of electrons among the subshells of the atom, and Hund’s rule of maximum multiplicity explains the filling of orbitals in the subshells.

The aufbau principle states that in the ground state, electrons fill atomic orbitals from lowest to highest energy to achieve the lowest-energy configuration.

Though energy generally increases with shell number, the greater penetration of s orbitals often leads to the four-s and five-s orbitals having lower energies than the three-d and four-d orbitals, respectively. The order can be remembered using diagrams like this one, where the path of the arrow reveals the sequence in which electrons are assigned to orbitals.

Consider writing the electron configuration for carbon — an element with atomic number six. Certainly, the 1s orbital, which has the lowest energy, should be filled before the 2s orbital. Each orbital can hold a maximum of two electrons.

The fifth electron enters a 2p subshell. But which of the three 2p orbitals does it populate?

Well! The orbitals in any subshell are presumed to be degenerate, which means that they have the same energy. Thus, the fifth electron can enter any of the three degenerate 2p orbitals.

What about the sixth electron? Does it enter the 2p orbital with an electron or one of the vacant 2p orbitals?

According to Hund’s rule of maximum multiplicity, electrons singly occupy all orbitals of a given energy level before they start pairing, and the unpaired electrons cannot have opposite spins: their spins must be parallel.

Hence, for carbon, the two 2p electrons must occupy two different orbitals and have parallel spins. This way, electrons can spread over a larger area. This decreases their shielding of each other, thereby minimizing the energy of the atom.

For nitrogen, each of the three 2p orbitals is singly occupied.

For oxygen, once the degenerate 2p orbitals are filled singly, the last electron must pair with another 2p electron. The atom has two unpaired electrons.

The electron configuration of neon reveals that the outermost shell is filled to its maximum capacity of eight electrons. Neon has two electrons, called core electrons in the inner shell, and eight electrons, called valence electrons, in the outermost shell.

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To determine the electron configuration for any particular atom, we can build the structures in the order of atomic numbers. Beginning with hydrogen,…