Question

Complete the following orbital diagrams for the groundstate electron arrangement for aluminum, chlorine, and sulfur. Be sure to follow the three orbital filling rules: the aufbau principle, the Pauli exclusion principle, and Hund's rule. \(\mathrm{Al}\) \(\mathrm{Cl}\) S

Short answer

Aluminum (13 electrons): 1s - 2 electrons, 2s - 2 electrons, 2p - 6 electrons, 3s - 2 electrons, and 3p - 1 electron. Chlorine (17 electrons): 1s - 2 electrons, 2s - 2 electrons, 2p - 6 electrons, 3s - 2 electrons, and 3p - 5 electrons. Sulfur (16 electrons): 1s - 2 electrons, 2s - 2 electrons, 2p - 6 electrons, 3s - 2 electrons, and 3p - 4 electrons.

Step-by-step solution

Aluminum (Al), atomic number 13

Atomic number indicates there are 13 electrons in the neutral atom. To arrange them in the orbitals: 1s gets 2 electrons, 2s gets 2, 2p gets 6 (2 each in 2p_x, 2p_y, 2p_z), 3s gets 2, and 3p gets 1 (in 3p_x).

Chlorine (Cl), atomic number 17

Cl has 17 electrons. First 2 go to 1s, next 2 to 2s, next 6 to 2p (2 each in 2p_x, 2p_y, 2p_z), next 2 to 3s, and next 5 to 3p (2 in 3p_x, 2 in 3p_y and 1 in 3p_z).

Sulfur (S), atomic number 16

S has 16 electrons. First 2 go to 1s, 2 each go to 2s, 2p_x, 2p_y, and 2p_z (total 8 in 2p), 2 go to 3s, and next 4 go to 3p (2 in 3p_x, 2 in 3p_y).

Key concepts

Aufbau Principle

The Aufbau Principle is a key concept used when filling an atom's electron orbitals in a specific order. It essentially tells us to "build up" the electron configuration, starting with the lowest energy orbital and working our way up. This order is influenced by the increasing energy levels of orbitals.

Each electron occupies the lowest available energy orbital. For example, an atom starts to fill the 1s orbital, then 2s, followed by 2p, 3s, and so on. This rule helps in outlining the sequence in the step-by-step solution where, for instance, aluminum fills its 1s, then 2s, 2p, and progresses up to its 3p orbital.

• Electrons occupy the lowest energy orbitals first.
• Use the 'n+l' rule to determine the order: Orbitals with lower (n+l) values get filled first. If two orbitals have the same (n+l) value, the one with a lower 'n' fills first.

Pauli Exclusion Principle

The Pauli Exclusion Principle is crucial in determining the electron configuration within an orbital. Simply put, it states: no two electrons in an atom can have the same set of all four quantum numbers. This takes care of the uniqueness in electron arrangement.

In practical terms, this means that each orbital can hold a maximum of two electrons and they must have opposite spins. This is vital for filling strategies as seen in the solutions. If we look at chlorine, in its 2p orbitals, it accommodates two electrons per orbital, each with opposite spins.

• Each orbital holds a maximum of 2 electrons.
• Electrons must have opposite spins \(\uparrow\downarrow\).

Hund's Rule

Hund's Rule is all about maximizing electron spin alignment in a sublevel with multiple orbitals, like 'p' or 'd'. It essentially ensures that every orbital in a sublevel receives one electron before any gets a second. This approach keeps electrons unpaired as much as possible, minimizing electron-electron repulsion.

For example, when filling the 2p orbitals in sulfur, electrons are first distributed singly across the three available 2p orbitals before any pairing occurs. This aligns with Hund's strategy to minimize energy and maximize stability.

• Electrons fill empty orbitals singly first.
• This minimizes electron-electron repulsions and results in a lower energy configuration.