Identify what is wrong with each electron configuration and write the correct ground-state (or lowest energy) configuration based on the number of electrons. (a) \(1 s^{4} 2 s^{4} 2 p^{12}\) (b) \(1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 3 d^{10}\) (c) \(1 s^{2} 2 p^{6} 3 s^{2}\) (d) \(1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 4 s^{2} 4 d^{10} 4 p^{3}\)

The Aufbau principle is a fundamental concept used to determine the electron configuration of an atom in its ground state, which refers to the most stable, lowest energy arrangement of its electrons. According to this principle, electrons are added to atomic orbitals in order of increasing energy, starting with the lowest energy orbital. Electrons prefer to occupy empty orbitals first before pairing up with others.

The name 'Aufbau' is derived from the German word 'aufbauen,' which means 'to build up.' The principle guides the placement of electrons into the orbitals in a way that energy is minimized, starting with 1s, then 2s, followed by 2p, 3s, and so forth, filling each orbital according to their increasing energy levels. The sequence in which the orbitals are filled can be remembered using the Madelung rule or by consulting the periodic table, which hints at the order based on electron configurations of the elements.

Applying the Aufbau Principle

When working with electron configurations such as in the exercise, recognizing the pattern of filling ensures that students can identify when an electron configuration does not align with the Aufbau principle. For instance, the suggested configuration for element (d) in the exercise '1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 4d¹⁰ 4p³' is incorrect because it skips filling the 3d subshell before starting with 4d, which goes against the Aufbau principle.

The ground-state configuration represents the lowest energy arrangement of electrons in an atom's orbitals. Electrons fill up orbitals starting from the lowest energy level, minimizing the energy of the atom and making it more stable. The ground-state configuration is important not only for predicting chemical properties of elements but also in understanding their reactivity and bonding behavior.

Every element has a unique ground-state configuration that can be predicted using the rules of quantum mechanics, including the Aufbau principle, Pauli's exclusion principle, and Hund's rule of maximum multiplicity. The ground state implies that the atom is at its most relaxed energy level, without any external energy input triggering excitations. Incorrect electron configurations, like the ones presented in the exercise, often fail to represent this state accurately, leading to fundamentally flawed understandings of an element's behavior.

Ground-state Corrections

Correcting a flawed ground-state configuration is simple once you are familiar with the order of subshell filling and subshell capacities. For example, the corrected configuration for element (a) from the exercise reflects a step-by-step application of the Aufbau principle and correctly places electrons up to the 3p subshell, resulting in a stable ground-state.

Subshells are divisions within electron shells of an atom that correspond to different sets of orbitals. Each type of subshell (s, p, d, and f) has a specific capacity for how many electrons it can hold, based on the number and arrangement of orbitals within it. The maximum number of electrons that each type of subshell can hold is dictated by quantum mechanics: an s subshell can accommodate 2 electrons, a p subshell can hold 6, a d subshell can have up to 10, and an f subshell can carry 14.

These capacities are critical to understanding and writing the correct electron configurations, as it dictates the order of how electrons are distributed among the orbitals. When assigning electrons to subshells, students must ensure not to exceed these capacities, which is a common mistake seen in the original exercise where configurations like '1s⁴' or '2p¹²' exceed the allowable electron capacity for those subshells, leading to incorrect configurations.

Correcting Subshell Capacities

Identifying subshell capacity errors is often the first step in correcting electron configurations. By understanding that each subshell type has a strict limit on electron occupancy, one can use this knowledge, together with the Aufbau principle, to amend incorrect configurations to display the proper ground-state electron configuration for any given number of electrons.