Damien has a master's degree in physics and has taught physics lab to college students.
Hund's rule, the Pauli exclusion principle, and the Aufbau principle are the three rules governing how electrons fit in the atomic structure. In this lesson, we will learn how these rules work and how they relate to the four quantum numbers.
Review of Quantum Numbers
At this point in studying chemistry, when you visualize an atom, you likely think of a nice orderly structure with a nucleus of positively charged protons and neutral neutrons that are orbited by rings of electrons, much like the structure of the solar system with planets orbiting the sun. This model of an atom follows the Bohr model, which has a positively charged nucleus of protons and neutrons surrounded by fixed rings of electrons called shells.
We can think of atomic structure like a hotel. Just like there are a fixed number of rooms where guests may stay, there are fixed locations where we are likely to find electrons. These fixed locations are called orbitals and their location is defined by their quantum number. Quantum numbers allow us to define the location of an electron within the atomic structure. Much like a hotel room, the orbitals are located at different floors, or levels, of the structure, and can even be described by the shape of the wing in which they are located.
In this model, the shells correspond to energy levels in the atomic structure, with the shells closer to the nucleus having the lowest energy level. This energy level is also defined as the first quantum number, n. So, an electron in the first shell would have a first quantum number (or n) of one. If it was in the second shell, it would have a quantum number of two, and so on. If you think of our hotel analogy, the levels towards the bottom take the least amount of energy to get to, and thus these levels have the lowest energy.
Within each shell, we find subshells that have different shapes depending on their energy level and thus can fit a different number of electrons. They are named after the letters s, p, d, f and so on. These subshells are the second quantum number and are numerically defined as follow:
letter = level (l)
s = 0
p = 1
d = 2
f = 3
The first shell has just the s subshell. The second has s and p. The third has s, p, and d. The higher the first quantum number or the shell, the more subshells and thus electrons can fit into that structure.
The third quantum number, m sub l, specifies the orientation of a specific orbital at a given n and s. This quantum number allows us to break up each subshell into individual orbitals of two electrons each. We can calculate the number of orbitals by the equation 2l + 1. Thus, according to this equation, the s shell would have 1 orbital with 2 electrons. The p shell would have 3 orbitals with 6 electrons. The d shell would have 5 orbitals with 10 electrons. The f would have 7 orbitals with 14 electrons.
Pauli Exclusion Principle
So, according to these rules, if we look at the first shell, it only contains two electrons in the first subshell. The quantum number can be described as 1s^2. However, another rule is that two electrons cannot have identical quantum numbers. So, if two electrons have to fit inside one s subshell, how will this work?
This matter directly relates to the Pauli Exclusion Principle, which states that two electrons cannot exist in the same location and thus electrons in the same orbital must have opposing spins. Hydrogen only has one electron in the 1s orbital and has a quantum number of 1s^1. Helium has two electrons in this field, so they must have opposing spins, and it has a quantum number of 1s^2.
This spin factor is the fourth quantum number, ms, and is described as either +1/2 for a spin 'up' or -1/2 for a spin 'down.'
So now that we've reviewed the orbital structure, let's dive in to how the electrons fill these orbitals. Because electrons are both negatively charged, there is a certain amount of repulsion that prevents them from wanting to fill the same space. So, according to Hund's Rule, electrons will fall into empty orbitals of the same energy before electrons begin to pair up into the same orbital.
Closely related to Hund's Rule is the Aufbau Principle, which states that electrons will fill the lower energy levels before moving to higher energy orbitals. Remember that each orbital has two electrons and the number of orbitals at an energy level depends on the first two quantum numbers.
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Let's combine Hund's Rule and the Aufbau Principle by looking at the electron configuration for two very common elements. Nitrogen has an atomic number of 7 and thus has 7 protons and electrons. Next to it on the periodic table is oxygen with an atomic number of 8 and thus 8 protons and electrons. The s subshells are lower energy in the first and second shells and thus fill first. The p subshell is filled with one electron each in nitrogen; however, since oxygen has four electrons that go into this subshell, only when the three orbitals already have one electron does it completely fill an orbital.
In general, the energy levels of the orbitals increase with the first and second quantum numbers, which are the shell and the subshell. However, as you start getting to higher energies, this relationship gets more complicated because the s subshells of higher levels may have lower energy than the d and f subshells of lower levels. The lines on this diagram show the direction of increasing energy:
This chart can be used to determine quantum number.
You will notice that the 4s subshell has lower energy than the 3d subshell. You do not have to memorize these relationships, but just remember that when you start getting to the higher energy levels, consult this chart to help you determine the quantum number.
In summary, Hund's Rule, the Aufbau Principle, and the Pauli Exclusion Principle help us define how electrons fill the orbitals within an atomic structure. This helps us predict the location of electrons in an atom as we increase the number of electrons. The Pauli Exclusion Principle states that no two electrons can have the same quantum number, and thus, electrons in the same orbital must have opposite spins. Remember the quantum number is the numerical description of the likely location of the electron, so you can think of it as the electron's address.
The Aufbau Principle states that electrons fill orbitals of lower energy first before moving to higher energy orbitals. So you must fill all of the orbital spaces in the 2s orbital before moving on to the 2p orbitals.
Finally, Hund's Rule says that because of the repulsion between the two negatively charged electrons, a newly added electron will go into an empty orbital of the same energy before going into an orbital that already has an electron present. These rules help us predict how the orbital spaces will be filled by elements on the periodic table as we move to larger elements with more electrons.
Following this lesson, you'll have the ability to:
Define electron shells, orbitals and quantum numbers
Recall what the Bohr model is
Describe the Pauli Exclusion Principle, Hund's Rule and the Aufbau Principle
Explain how the three concepts above can be used to predict how orbital spaces will be filled with electrons
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