Atomic Orbitals — Energy Levels & Sublevels

Orbitals in Atoms

In the center of the atom is the nucleus made of protons and neutrons. Around the nucleus is the space where electrons exist. Electrons are always moving in this space.

The exact location of an electron at a given time cannot be pinpointed, so it is hard to find an electron. However, the most likely location of electrons are represented by atomic orbitals. Atomic orbitals represent where the electrons can be found, there are different types of orbitals which are shaped differently.

Energy Levels and Sub-levels

Every atomic orbital has an energy level. The energy level is denoted by $n$ where $n = 1, 2, 3, 4, ...$. As $n$ increases, the energy of the orbital increases.

There are four types of orbitals: $s, p, d, f$. Each type of orbital has different shapes. Each type of orbital has sub-levels, but each has a different amount: $s$= 1 sub-level, $p$= 3 sub-levels, $d$= 5 sub-levels, and $f$= 7 sub-levels.

Let's consider the energy level, $n= 2$. At this energy level there are two types of orbitals: $s$ and $p$. The three sub-levels of the $p$ orbitals are broken down into $x, y,$ and $z$. The $x, y,$ and $z$ represent the direction of the orbitals. For example $x$ would be a long the $x$-axis. The orbitals in $n=2$ are: $2s, 2p_x, 2p_y, 2p_z$.

To connect back to an atom we all know and love, the hydrogen atom would be at the energy level n=1. Therefore, hydrogen would only have a half-filled 1s orbital as it only has 1 electron. Remember that each orbital can hold 2 electrons. On the other hand, carbon would be at the n=2 energy level, so it would have $1s$, $2S$, and $2p$ orbitals. It's $1s$ and $2s$ orbitals would be full, but the $2p$ orbitals would not be filled. Therefore, hydrogen is more likely to have its electron closer to the nucleus than carbon since only its $s$ orbital is populated.

Mathematical Functions

Information about orbitals and electron location are described by mathematical equations. Erwin Schrödinger is well known for his theoretical experiment known as "Schrödinger's Cat", but he is also known for his work on atomic structures. Remember, de Broglie taught us that all matter had a wavelength. Schrödinger built on his work by, describing the movement of electrons as waves. Wave equations are used to represent this movement mathematically. Solving wave equations gives wave functions or orbitals ($\psi$). The square of a wavefunction ($\psi^2$) describes the probability of an electron occupying that space. When $\psi^2$ = 0, an electron has zero probability of being in that space. Spaces, where electrons are not found in an orbital, are called nodes.

What's the Point of Atomic Orbitals?

At this point, are you wondering, "so what?" Atomic orbitals are fascinating. But, it all seems a little theoretical. But, our knowledge of orbitals will pave the way for electron configurations. We want to understand an element's reactivity. To do that, we need to know where an atom's electrons are. For example, consider the periodic table. The elements on the far left behave very differently from the far right. An alkali metal like sodium wants to give up an electron. But, a halogen, like chlorine, wants to steal an electron. As we continue to learn, you'll use atomic orbitals to predict chemical bonding!

(Video) Atomic Orbitals, Visualized Dynamically

by The Science Asylum

In this video, Nick explains atomic orbitals. He starts by talking about the atom. We know they consist of protons, neutrons, and electrons. But, the nucleus is minuscule. They average between 1 and 10 femtometers! In scientific notation that $1\times 10^{-15}$ meters! What about the electrons' orbitals? They're 100,000 times larger! That's why they determine most of the chemical properties and chemical reactions.

Next, Nick briefly reviews the historical electron models. Physical chemists had so many unique hypotheses! We had to get past the plum pudding and Bohr models before arriving at the quantum mechanical model. Quantum mechanics changed everything! Now we had to think of probability. Nick explains and shows orbitals in terms of probability.

But, how do we define probability? From the Schrodinger equation! Nick demonstrates that the Schrodinger equation is just the conservation of energy. But, it's applied to quantum systems. That's how we end up with the different quantum numbers)! He explains a little of the math. Then, he demonstrates that changes in quantum states are just changes in probability. For example, its probability changes when an electron absorbs or emits a photon. But, in quantum mechanics, probability relates to energy. So, the probability is a conserved quantity!

In general, we use orbitals to predict the region of space an electron may be in. To tie this back to quantum mechanics and the wave-particle duality, orbitals are another term for the wavefunction of an electron. In other words, an orbital represents the probable regions of space an electron is in. It represents the electron density around an atom. Remember that the electron is in all of those places at once since we can think of light as both a wave and a particle when using quantum mechanics.