Write electron configurations for each element. Use the symbol of the previous noble gas in brackets to represent the core electrons. (a) \(\mathrm{Te}\) (b) \(\mathrm{Br}\) (c) \(\mathrm{I}\) (d) \(\mathrm{Cs}\)

Understanding how to write electron configurations is a fundamental part of mastering chemistry. The process involves determining the distribution of electrons of an atom or molecule in atomic or molecular orbitals. Each electron is represented by arrows or numbers indicating the spin and placement within an energy level and sublevel.

Imagine the atom as a set of shelves, with each shelf representing a principal energy level. These shelves have boxes (orbitals), where you can place up to two electrons, which must have opposite spins. The method we use to place the electrons in the boxes follows three important rules: the Aufbau principle, Pauli exclusion principle, and Hund's rule.

The Aufbau principle guides us to fill the lowest energy levels first, much like filling the lower shelves before the upper ones. Pauli exclusion principle tells us that each box can hold a maximum of two electrons, but they must have opposite spins, like fitting two gloves in a box, one for the right hand and one for the left. Hund's rule suggests that when electrons are added to a sublevel with more than one orbital, one electron is added to each orbital before any pairing occurs, just like passengers preferring to sit alone before sharing a double seat on a bus.

In exercises such as finding the electron configuration for tellurium (\text{Te}), which falls after the noble gas krypton (\text{Kr}), we follow these rules. Starting after the noble gas configuration for Kr, electrons fill up the 4d, then 5s, and partially fill the 5p orbitals to arrive at the final configuration for Te: [\text{Kr}]\(4d^{10}5s^{2}5p^{4}\).

The Nobel Gas Shorthand Notation is like using a shortcut in writing electron configurations by starting with the closest noble gas that precedes the element in the periodic table. Why use a shortcut? This is because noble gases have completed electron configurations, which makes them stable reference points.

For instance, the electron configuration for bromine (\text{Br}) formally begins from the very first element, hydrogen, and goes on until we place the 35th electron. However, to simplify, we find the noble gas with the closest lower atomic number, which is krypton (\text{Kr}), and use its configuration as our starting point. From that, we continue adding the remaining electrons in their proper orbitals. Thus, bromine’s configuration becomes [\text{Kr}]\(4s^{2}3d^{10}4p^{5}\), neatly packaged using the noble gas shorthand notation.

Why is it useful?

Using noble gas shorthand not only saves time but also reduces the potential for error when writing very long electron configurations. Plus, it gives an immediate understanding of valence electrons which are critical in predicting chemical properties.

Orbital filling order is the sequence in which orbitals are filled with electrons. To know the order, picture the periodic table and the diagonal rule also known as the 'nifty trick' of slanting lines that guide us in knowing which orbital to fill next.

Here's how it goes: We start at hydrogen and fill the 1s orbital. We then move to helium, still in the 1s orbital. For lithium, we enter a new shelf and start filling the 2s orbital, and so on. As you might expect, the order is 1s, 2s, 2p, 3s, 3p, 4s, and it continues with the 's' orbitals always being filled first at each new energy level followed by the 'p', 'd', or 'f' orbitals respectively, consistent with the filling sequence of the diagonal rule.

For cesium (\text{Cs}), as we can observe from the step by step solution, the electron configuration starts after the noble gas xenon (\text{Xe}). Since Cs is the first element in its period, we are beginning a new shelf and therefore only need to add a single electron to the 6s orbital, resulting in [\text{Xe}]\(6s^{1}\). This follows the orbital filling order, and knowing this order is crucial for writing accurate electron configurations.