High School Chemistry/Aufbau Principle

Everything in the universe is driven to minimize its potential energy. Previously we learned that heavy objects fall when they're dropped, because their total potential energy is lower on the ground than it is when they're hovering in the air. That's why Wile E. Coyote could drop an anvil on Road Runner – he knew that the anvil would fall, because falling would lower its potential energy. It's the same with a bowling ball placed on a hill. At the top of the hill, the bowling ball has more potential energy than it does at the bottom, so you can always bet on the bowling ball rolling down the hill rather than up the hill, because the bowling ball will always try to minimize its energy. In this lesson, we won't look at heavy objects like bowling balls and anvils. Instead, we'll look at tiny objects – we'll look at electrons. Even though electrons are much, much smaller than anvils and bowling balls, the same principle applies. An electron will do anything that it can to lower its potential energy.

Lesson Objectives

 * Explain the Aufbau Principle.
 * Given two different orbitals, predict which the electron will choose to go into.

Electrons are Found in Energy Levels with Increasingly Higher Energy
Whenever an electron is found inside an atom, it exists in what’s known as an orbital. By now, you should know what an orbital is. An orbital describes a particular region of space within the atom where the electron is most likely to be found. While orbitals are important when it comes to figuring out an electron's probable location, they are equally important when it comes to figuring out an electron's energy. Electrons in different orbitals frequently have different energies. Of course, an electron is never going to "choose" to be in an orbital that has a higher energy if there's space available in an orbital that has a lower energy. It's a lot like you riding the bus. You would never choose to waste energy walking 20 miles to school provided there was space for you on the bus. If there wasn't any space on the bus, though, you may be forced to walk. It's the same with electrons.

As pictured below, if there's no room on the bus, you may be forced to walk. It's the same with electrons. If there's no room in a low energy orbital, they may be forced into a higher energy orbital.



The fact that electrons always fill up lower energy orbitals first has important consequences when it comes to determining which orbitals contain electrons in any given atom.

Remember that the principal quantum number, n, is associated with the "energy level" of the electron. Electrons with standing waves described by bigger values of n had higher energies, while electrons with standing waves described by smaller values of n had lower energies. If you were an electron, then, and you had the choice of being in an orbital with n = 1 or an orbital with n = 2, which would you choose? Obviously you'd choose to be in the orbital with n = 1, because it has a smaller value of n, and thus a lower energy (remember, both people and electrons prefer to be in states with lower energy).

Naturally, there is a limit to the total number of electrons that can exist in the same atom at the n = 1 energy level. In fact, it turns out that there can be at most two electrons with n = 1 in any given atom. That's because there is only one n = 1 orbital per atom. Of course, there are many atoms with more than two electrons. Lithium, for instance, has three. What happens to the electrons in an atom like lithium? Obviously, the first two electrons are going to occupy the single orbital that exists at the n = 1 energy level. Since this orbital only has room for two electrons, though, the third electron has to move up to the n = 2 energy level. In other words, electrons will fill up orbitals in order of increasing energy. If there's space at the n = 1 energy level, that space will be filled before any electrons move into the n = 2 energy level. Similarly, if there's space at the n = 2 energy level, that space will be filled before any electrons move into the n = 3 energy level.

In an Energy Level Electrons are Assigned to Sublevels with Increasingly Higher Energy
So far you know that an electron will always be found occupying the orbital in the first energy level, rather than the second energy level, provided that there is space available. Similarly, an electron will be found occupying the second energy level, rather than the third energy level, provided that there is space available. But what about electron sublevels? Among the orbitals with the same value of n, the s orbital will always be filled first, followed by the p orbitals (and then the d orbitals).

We can summarize these rules with the following statement: Electrons will fill available orbitals starting with those at the lowest energies before moving to those at higher energies. This statement is known as the Aufbau Principle. That may sound like a funny name, but "aufbau" is actually the German word for "construction", and the Aufbau Principle describes how the orbitals are "constructed" by progressively adding electrons to higher and higher energy levels.

Before we move on and consider exactly how many electrons go into each energy level, and sublevel, it's important to point out how the energies of the electrons in an atom relate to the energy of the entire atom itself. If each electron tries to minimize its energy by going into the lowest energy orbital available, then the total energy of all the electrons in the atom is also as low as possible.

Let's compare electrons minimizing their energy in an atom to your relatives minimizing their energy consumption in your family. If you do your best to turn off the lights and save as much energy as possible, and your brother does his best to turn off the lights and save as much energy as possible, and your sister does her best to turn off the lights and save as much energy as possible, and your parents also do their best to turn off the lights and save as much energy as possible, then collectively, your entire family is saving as much energy as possible as well. It's the same with electrons. If the first electron fills the lowest energy orbital available to it, and the second electron fills the lowest energy orbital available to it, and the third electron fills the lowest energy orbital available to it, and the fourth electron also fills the lowest energy orbital available to it, then collectively, the entire atom is in the lowest energy state possible as well.

Just as you would prefer to minimize your energy by sleeping, or riding a bus, electrons minimize their energy by occupying the lowest energy orbital available to them and atoms minimize their energy by having all of their electrons in the lowest energy "configuration" (arrangement) possible. Later, you will learn that practically all chemical processes rely on this same principle of energy minimization.

Lesson Summary

 * In an atom, electrons will fill up orbitals in order of increasing energy.
 * The principle quantum number determines the "energy level" of the orbital. Orbitals with lower values of n are usually associated with lower energy and will be filled first.
 * The azimuthal quantum number determines the "sublevel" of the orbital.
 * Orbitals with lower values of ℓ (but the same value of n) are always associated with lower energy and will be filled first.
 * The Aufbau Principle states that electrons will fill available orbitals starting with those at the lowest energies before moving to those at higher energies.
 * Since each electron in an atom minimizes its energy, the energy of the entire atom is a minimum as well.

Review Questions

 * 1) While we have talked about emission spectra, another type of spectra is known as absorption spectra. In emission spectra, the atom emits lines of light like those you saw in the examples of atomic spectra. In absorption spectra, the atom absorbs lines of light, rather than emitting them. Can you explain this in terms of electrons and orbitals? What do you think the relationship between absorption spectra and emission spectra might be?
 * 2) If an electron has a "choice" between going into an orbital in the n = 1 energy level or an orbital in the n = 2 energy level, which do you think it chooses?
 * 3) If an electron in the n = 3 energy level has a "choice" between going into an orbital with ℓ = 0 or an orbital with ℓ = 1, which do you think it chooses?
 * 4) Select the correct statement. According to the Aufbau Principle…
 * (a) orbitals with higher values of n fill up first.
 * (b) orbitals in the same energy level, but with higher values of ℓ fill up first.
 * (c) orbitals with lower values of n fill up first.
 * (d) it is impossible to predict which orbitals will fill up first.
 * 1) Decide whether each of the following statements is true or false.
 * (a) Electrons in different orbitals have different energies.
 * (b) An electron will enter an orbital of higher energy when a lower energy orbital is already filled.
 * (c) For some atoms the first energy level can contain more than two electrons.
 * 1) Does the electron in the hydrogen atom absorb or emit energy when it makes a transition between the following energy levels:
 * (a) n = 2 to n = 4
 * (b) n = 6 to n = 5
 * (c) n = 3 to n = 6
 * 1) Fill in the blanks. There is one s orbital, three p orbitals, and five d orbitals in the n = 3 energy level of an atom. If a particular atom has a total of 5 electrons in the n = 3 energy level, then there are…
 * (a) ___ electrons in the s orbital
 * (b) ___ electrons in p orbitals
 * (c) ___ electrons in d orbitals
 * 1) Fill in the blanks. There is one s orbital, three p orbitals, five d orbitals and 7 f orbitals in the n = 4 energy level of an atom. If a particular atom has a total of 7 electrons in the n = 4 energy level, then there are…
 * (a) ___ electrons in the s orbital
 * (b) ___ electrons in p orbitals
 * (c) ___ electrons in d orbitals
 * (d) ___ electrons in f orbitals
 * 1) According to the Aufbau rule, which of the following atoms has a sub-shell that is exactly half-filled?
 * (a) Ba
 * (b) Al
 * (c) C
 * (d) As
 * (e) O

Vocabulary

 * Aufbau principle
 * Electrons will fill available orbitals starting with those at the lowest energy before moving to those at higher energies.