Without referring to the text, write the ground-state electron configurations of the first-row transition metals. Explain any irregularities.

When students begin to learn about electron configurations, the Aufbau principle serves as a fundamental guideline. This principle, sometimes referred to as the building-up principle, asserts that as protons are added one by one to the nucleus to build up elements, electrons are similarly added to hydrogen-like orbitals.

According to the Aufbau principle, electrons occupy the lowest available energy levels before filling higher levels. This concept is visually represented in an Aufbau diagram, which organizes orbitals in order of increasing energy from bottom to top. Electrons first fill the 1s orbital, then move on to 2s, 2p, 3s, and so forth, following a specific sequence known as the Madelung rule or diagonal rule.

One valuable exercise improvement tip is to use a periodic table to trace the electron filling order—doing this alongside an Aufbau diagram can reinforce your understanding of why electrons arrange themselves in the way they do. Remember that the Aufbau principle is an approximation; while it gives good predictions about electron configurations, some irregularities can occur, especially among transition metals.

The set of elements from Scandium (Sc) to Zinc (Zn) on the periodic table are collectively known as first-row transition metals. These metals are characterized by the filling of their 3d orbitals with electrons, which is the defining property of transition metals. When writing out the electron configuration of these elements, one can often start with the expectation that the 4s orbital gets filled before the 3d orbital because of its lower energy when the atom is in isolation.

By applying the Aufbau principle as a starting point, one notices the sequence in which orbitals are expected to be filled, with the aim of following the lowest energy path. However, special attention is needed due to the quirks that arise with these elements. It can be beneficial for students to memorize the electron configurations of first-row transition metals, but even more advantageous is developing a deep understanding of the underlying principles guiding these arrangements.

While the Aufbau principle provides a solid foundation for predicting electron configurations, it is important to note that irregularities do exist, particularly among transition metals. These irregularities stem from the complex interplay between electron-electron repulsions and orbital energies.

Two notable examples include Chromium (Cr) and Copper (Cu), whose electron configurations are not what one might initially predict using the Aufbau principle alone. Chromium is expected to have an electron configuration ending in \(3d^{4}\) \(4s^{2}\), and Copper is expected to end with \(3d^{9}\) \(4s^{2}\). However, these elements favor an electron configuration that minimizes repulsions and maximizes subshell symmetry and stability – thus, Chromium opts for \(3d^{5}\) \(4s^{1}\) and Copper for \(3d^{10}\) \(4s^{1}\).

Why does this happen? For Chromium, having a half-filled d-subshell (\(3d^{5}\)) offers a more balanced distribution of electrons, reducing electron repulsion and thus lowering the energy. In the case of Copper, a completely filled d-subshell (\(3d^{10}\)) achieves a stable electron configuration.

These irregularities serve as excellent examples of how reality can diverge from theoretical predictions, motivating students to understand the principles rather than just memorize configurations. When dealing with irregularities, an exercise improvement tip is to visualize and draw out the energy levels, emphasizing the higher stability of half-filled and completely filled subshells.