Write the ground state electron configuration for each atom and ion pair. a. Zr, Zr2+ b. Co, Co2+ c. Tc, Tc3+ d. Os, Os4

The Aufbau principle is a fundamental guideline used to determine the electron configuration of an atom in its ground state. The name 'Aufbau' comes from the German 'Aufbauen', meaning 'to build up'. According to this principle, electrons fill atomic orbitals starting with the lowest energy levels before filling higher energy levels.

There is a specific order in which the orbitals are filled: 1s, 2s, 2p, 3s, 3p, and so on. This is the order used in the step by step solution to establish the electron configurations of elements like Zirconium (Zr), Cobalt (Co), Technetium (Tc), and Osmium (Os).

An easy way to remember the order is by using the diagonal rule. Picture the periodic table and draw diagonal lines from the top right to the bottom left. Orbitals on the same diagonal are filled successively. One aspect to note, particularly for transition metals and their ions, is that the 4s orbital is filled before the 3d, but when ions form, electrons are usually removed from the 4s orbital first, reflecting its higher energy when compared to the 3d in the ionized state.

The atomic number of an element is of prime importance when establishing its electron configuration. It is denoted as 'Z' and corresponds to the number of protons found in the nucleus of an atom. For neutral atoms, the atomic number also equals the number of electrons, which is essential in writing electron configurations.

As seen in the step by step solution, to find the electron configuration of Zr, Co, Tc, and Os, one must first ascertain their atomic numbers—40, 27, 43, and 76, respectively. Knowing these values allows determination of the number of electrons that need to be distributed across the orbitals according to the Aufbau principle. When dealing with ions, the electron count is adjusted by the charge to represent loss or gain of electrons.

The Pauli exclusion principle is another crucial factor influencing electron configuration. This principle states that no two electrons in an atom can have the same set of four quantum numbers. Essentially, this rule means each orbital can hold a maximum of two electrons and they must have opposite spins. This is represented in the electron configuration notation where orbitals are written with a maximum superscript of '2'.

For instance, in the configurations for Zirconium (Zr) and Cobalt (Co), each s, p, d, and f subshell follows this rule. The Pauli exclusion principle ensures that when writing electron configurations for ions, each electron removed comes from an orbital with an existing electron, thereby maintaining compliance with this fundamental quantum rule.

Hund's rule is about electron distribution in degenerate (equal energy) orbitals. It stipulates that electrons must occupy all the orbitals in a subshell singly before any orbital is doubly occupied. Additionally, all electrons in singly occupied orbitals must have the same spin direction. The significance of Hund’s rule lies in minimising electron repulsion and maintaining the lowest energy configuration of an atom.

When applying Hund's rule to the ground state electron configurations of neutral atoms, it affects the arrangement within subshells having multiple orbitals such as the 3d in Cobalt (Co) and the 5d in Osmium (Os). For example, in Technetium (Tc), 5 electrons are distributed across the five 4d orbitals before any pairing occurs, in adherence to Hund’s rule. This rule is fundamental in defining the electronic structure and understanding the magnetic properties of the elements.