What is an 'electron'?

At the very heart of understanding the behavior of matter on the smallest scales lies the study of subatomic particles. These are the constituents of atoms which include protons, neutrons, and electrons. Protons and neutrons form the nucleus of an atom, while electrons, the focus of our initial exercise, orbit around the nucleus.

Electrons are vital to the structure of an atom as they determine how atoms will interact with each other to form molecules. The unique properties of each element depend significantly on the number and arrangement of electrons orbiting the nucleus. Due to their negative charge and low mass, electrons are also the primary carriers of electricity in many materials.

Atomic orbitals are regions in an atom where there is a high probability of finding electrons. These are not fixed paths but rather cloud-like zones around the nucleus where electrons reside according to the rules of quantum mechanics. Orbitals come in different shapes, most commonly denoted as s, p, d, and f orbital shapes. Each orbital can hold two electrons, each with a different spin.

The configuration of these orbitals is central to chemical bonding and the periodic properties of the elements. Electrons fill orbitals in a way to minimize the energy of the atom, which is why they first occupy the lower energy orbitals before moving to higher ones, a concept known as the Aufbau principle.

Wave-particle duality is a fundamental concept of quantum mechanics, revealing that every particle or quantum entity can exhibit both wave and particle characteristics. This duality is best illustrated by electrons — which we might think of as particles in their role in electricity, but also show interference patterns like waves in experiments such as the double-slit experiment.

This dual nature complicates our understanding of electrons because they can't be precisely pinned down in space; instead, we use probabilities to talk about where they might be found, which is described by their wave function. The wave-particle duality of electrons is a key insight that challenges our classical intuitions and demonstrates the non-intuitive behavior of the quantum world.

Electricity is a form of energy resulting from the existence of charged particles, such as electrons, which can flow through conductors like copper wires. It's what powers our homes, industries, and modern technology. At its core, electricity involves two key elements: current and voltage. Current (measured in amperes) is the flow of electrons and voltage (measured in volts) is the potential difference that motivates this flow.

The movement of electrons from one atom to another is the fundamental process that underlies all electrical circuits. By harnessing the flow of electrons, electrical circuits can do useful work, from lighting a bulb to running a computer. A thorough grasp of these fundamentals is necessary for diving deeper into any study of electronics and electrical engineering.

Electrical conductivity is the measure of a material's ability to allow the flow of electric current. In metals, conductivity is high due to the presence of free electrons in a 'sea of electrons' model. These free electrons originate in the conduction band, a band of energy levels in atoms where electrons are not bound to any particular atom and can move freely under the influence of an electric field.

When a potential difference is applied across a metallic conductor, these free electrons drift from the negative side (higher potential) to the positive side (lower potential), carrying the current. This property is the cornerstone behind electrical technology, as a better understanding of conductivity allows for the development of better conductors and more efficient electronic devices.

Quantum mechanics is the branch of physics that deals with the behavior of matter and light on the atomic and subatomic scales. It provides the framework within which the peculiar behaviors of electrons, like wave-particle duality and the quantization of energy levels, make sense. Quantum theory describes how subatomic particles exist in a state of probabilities until measured, and it introduces the concept of quantum tunneling, entanglement, and superposition.

Understanding quantum mechanics is essential for explaining why electrons behave as they do in atomic orbitals, their role in chemistry and electricity, and the working principles behind modern electronics, such as transistors and semiconductors, which are at the heart of computers and other electronic devices.