Quantum Numbers on the Periodic Table | Definition & Overview

The electron configuration for each element shows where the electrons are located. These locations can be described by using four numbers, called quantum numbers. They are the principal quantum number (n), the angular momentum quantum number (l), the magnetic quantum number (ml), and the spin quantum number (ms). Each electron within an atom has a unique set of these four quantum numbers. The four numbers that describe the location of an electron can be thought of as the address of the electron.

The Principal Quantum Number

The principal quantum number (n) represents the shell or the main energy level that electrons are in. These shells show how far away an electron is from the nucleus. These are positive integers values from 1 to 7. These are the numbers written before the s, p, d, or f in an electron configuration. For example, the electron configuration of lithium is $1s^{2}2s^1$ This means there are electrons in the first and the second energy levels. The 1 before the $s^2$ is a principal quantum number showing that those electrons are in the first shell and the 2 before the $s^1$ is a principal quantum number showing that the electron is in the second shell or energy level.

The Angular Momentum Quantum Number

The angular momentum quantum number"l" represents the subshell. It also shows the shape of the orbital. It is given a letter of s, p, d, or f. These letters are written after the principal quantum number. The number of possible subshells is given by the angular quantum number, which is a number equal to n-1. The electron configuration for oxygen is $1s^{2}2s^{2}2p^4$. The electrons in the first energy level have an angular quantum number "l" = 0. This means that the electrons in that energy level are only found in the s orbital, as that corresponds so "l" = 0. The second energy level has "l" = 0 or 1 so it has s and p subshells.

"l"=0 is an s orbital which is a sphere shape. "l"=1 is a p orbital which has a dumbbell shape, "l" = 2 is a d orbital, and "l" = 3 is an f orbital. The lowest possible value is 0, and the highest is n-1. So for the principal quantum number of n = 2 the angular momentum quantum numbers can be 0 or 1, so it can have s and p subshells.

The Magnetic Quantum Number

The magnetic quantum number tells us the orientation of the orbital around the nucleus. Its value will be integers ranging from -"l" to +"l". When "l" = 0 there is only one value and that is zero. "l" = 0 would be an s orbital and the s-orbital is a spherical shape. When "l" = 1, the magnetic quantum number can be -1, 0, and + 1 which gives the three possible orientations of the dumbbell-shaped p orbitals around the axis. These can be on the x-axis, the y-axis, and the z-axis.

Orientations of the three p orbitals.

For the principal quantum number of n = 2, the values for "l" can be -2, -1, 0, 1, and 2. These would be the f orbitals and they have five different orientations. For the principal quantum number of n = 3, the values for "l" can be -3, -2, -1, 0, 1, 2, and 3. These would be the d orbitals and there are seven different orientations for these orbitals.

The Spin Quantum Number

The spin quantum number represents the angular momentum of an electron and it is +½ or -½. The electrons are not really spinning; they are just represented by up arrows and down arrows. If there are two electrons that are in one orbital, they have to have the opposite spin quantum number. So if one electron in an orbital already has a spin of +½, the other will be -½.

Find the quantum numbers for the last electron of magnesium. First, write the electron configuration: $1s^{2}2s^{2}2p^{6}3s^2$. The last electron is in the 3s orbital, so n = 3. Since it is in an s orbital "l" = 0 and $m_l$= 0. The spin quantum number or $m_s$s = $\frac{1}{2}$ or $-\frac{1}{2}$.

There are some other rules that help determine where the electrons will go in an atom and help determine the electron configurations. These are Hund's rule, the Pauli exclusion principle, and the Heisenberg uncertainty principle. Hund's rule says that when electrons are going into orbitals that have the same energy, one electron will go into each orbital before they double up. This is seen in the three p-orbitals. If there are two electrons in the p orbitals, they will each be in a different orbital. They will not double up until there are more than three electrons, then one will go in each orbital, and from there, the extras will start doubling up in ones that already have one electron. The Pauli Exclusion principle says that no two electrons can have the same four quantum numbers, so if two electrons are in the same energy level, subshell, and orbital, then they will have opposite spins.

The Heisenberg uncertainty principle says that it is not possible to know both the location of an electron and its velocity. So what we determine using quantum numbers and electron configurations is the probable location of the electrons. It is not possible to know exactly where they are, but there are some areas where they are more likely to be than others. Those areas are the orbitals.

The periodic table organizes elements based on their numbers of protons and the organization of their electrons. The electron configuration can be determined by where the elements are on the periodic table. The number of valence electrons, or outer shell electrons, is also determined by the periodic table and is what gives the elements many of the properties that they have. The electron configuration can be thought of as the address for the electrons, which is determined by a set of four numbers called quantum numbers. The quantum numbers can be determined by looking at the electron configuration. An example of an electron configuration is that of oxygen, which is $1s^{2}2s^{2}2p^4$ The first quantum number is the principal quantum number (n) which is the number before the s or the p. This corresponds to the energy level that the electron is in. These are integers from 1 to 7. The second quantum number is the angular momentum quantum number which determines the subshells. This is represented by "l" and is equal to n-1. So for n=1, that means that"l"=0, which is just an s orbital. The next quantum number is the magnetic quantum number ($m_l$) and this gives the orientation of the orbital and can have values from -"l" to "l" so if "l" = 1, then the value for $m_l$ is -1, 0, and 1. This means that there are three orientations for the p subshell. The final quantum number is the spin quantum number and that is represented by either +1/2 or -1/2.

There are also three rules that determine the quantum numbers for electrons and how electron configurations are written. Hund's rule says that if the orbitals have the same energy, one electron will go into each orbital before they start doubling up. The Pauli Exclusion Principle says that no two electrons can have the same four quantum numbers. The Heisenberg uncertainty principle says that we cannot know both the location and the velocity of an electron and that orbitals are just areas where the electrons are likely to be found.