Write full orbital diagrams and indicate the number of unpaired electrons for each element. (a) \(\mathrm{He}\) (b) \(\mathrm{B}\) (c) \(\mathrm{Li}\) (d) \(\mathrm{N}\)

When exploring the mesmerizing world of atomic structure, the Aufbau Principle acts as our trusty guide. This principle is essentially a map that tells us the sequence of 'pit stops' an electron takes as it embarks on its journey to find a home within an atom. In simple terms, it dictates that electrons will always 'settle down' in the lowest energy orbital that is available to them.

Picture a hotel with multiple floors: electrons are like guests who must check into the lowest empty room they find. For an electron, the first floor is the 1s orbital, which offers the coziest and most energy-efficient accommodations. As more electrons arrive, they continue to fill up the hotel, starting from the ground up – this is why helium, with its two electrons, fills the 1s room and stops there. Other elements follow the same pattern, filling the 2s 'rooms' before moving on to the more spacious, but also more energy-demanding, 2p 'suites' and beyond. Remember, the Aufbau Principle is relentless; no skipping floors or jumping to higher energy levels without filling the lower ones first!

Now, let's shift our focus to the concept of unpaired electrons. These are the 'lone rangers' of the electron world – they are single electrons that occupy an orbital by themselves without a partner to pair up with. Unpaired electrons are crucial because they play a significant role in the chemical properties of an element, including its magnetic properties and reactivity.

Why the spotlight on these lonesome electrons? Well, for starters, they're the ones that typically engage in chemical bonds. They are ready and willing to 'mingle' with other unpaired electrons from different atoms, leading to the formation of chemical compounds. They’re like individuals at a social gathering, searching for their perfect plus-one to dance with. In our hotel analogy, these would be guests enjoying a room all to themselves, potentially inviting other lone guests to join them, starting a party, or forming a bond, per se. For example, in the case of lithium, out of the three existing electrons, two are comfortably paired in the 1s orbital, while one sits solo in the 2s room, making it unpaired and eager to react.

Last but certainly not least, we must acquaint ourselves with Hund's rule, which is like the 'social protocol' that unpaired electrons follow when moving into an atom's multi-room orbitals, such as the 2p suite. Hund's rule states that if there are multiple orbitals of the same energy level, electrons will occupy them individually with parallel spins before any pairing occurs. It’s all about maintaining harmony and minimizing repulsion among these charged particles.

Imagine our hotel's 2p suite has three separate rooms. If three guests – or electrons – were to check into this suite, rather than sharing a room and stepping on each other’s toes, Hund’s rule would have them each claim a separate room first. This provides a greater sense of personal space (which electrons love), thus reducing electron 'squabbles' (repulsion). This happens with nitrogen, where three unpaired electrons each take a separate room in the 2p suite, enjoying the luxury of space before they consider pairing up. Remember, only after each room has at least one electron will they start sharing rooms. In essence, Hund's rule keeps electrons civil and organized, averting unnecessary drama by keeping them as far apart as possible until it's absolutely necessary to pair up.