What is the L quantum number for an F Orbital?

The orbital letters are associated with the angular momentum quantum number, which is assigned an integer value from 0 to 3. The s correlates to 0, p to 1, d to 2, and f to 3. The angular momentum quantum number can be used to give the shapes of the electronic orbitals.

The orbital names s, p, d, and f stand for names given to groups of lines originally noted in the spectra of the alkali metals. These line groups are called sharp, principal, diffuse, and fundamental.

The s orbitals are spherical, while p orbitals are polar and oriented in particular directions (x, y, and z). It may be simpler to think of these two letters in terms of orbital shapes (d and f aren't described as readily). However, if you look at a cross-section of an orbital, it isn't uniform. For the s orbital, for example, there are shells of higher and lower electron density. The density near the nucleus is very low. It's not zero, however, so there is a small chance of finding an electron within the atomic nucleus.

The electron configuration of an atom denotes the distribution of electrons among available shells. At any point in time, an electron can be anywhere, but it's probably contained somewhere in the volume described by the orbital shape. Electrons can only move between orbitals by absorbing or emitting a packet or quantum of energy.

The standard notation lists the subshell symbols, one after another. The number of electrons contained in each subshell is stated explicitly. For example, the electron configuration of beryllium, with an atomic (and electron) number of 4, is 1s22s2 or [He]2s2. The superscript is the number of electrons in the level. For beryllium, there are two electrons in the 1s orbital and 2 electrons in the 2s orbital.

The number in front of the energy level indicates relative energy. For example, 1s is lower energy than 2s, which in turn is lower energy than 2p. The number in front of the energy level also indicates its distance from the nucleus. The 1s is closer to the atomic nucleus than 2s.

Electrons fill up energy levels in a predictable manner. The electron filling pattern is:

1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f

• s can hold 2 electrons
• p can hold 6 electrons
• d can hold 10 electrons
• f can hold 14 electrons

Note that individual orbitals hold a maximum of two electrons. There can be two electrons within an s-orbital, p-orbital, or d-orbital. There are more orbitals within f than d, and so on.

In this tutorial on quantum numbers, you will learn how we can describe the properties of an electron in an associated atom. These various properties include energy level, shape, orientation, and spin. You will also learn about orbital shapes.

Topics Covered in Other Articles

• Electron Configuration
• Orbitals & Orbital Shapes

Vocabulary

Nodes = a point or plane of zero electron density

Introduction to Quantum Numbers & Orbital Shapes

Quantum numbers are used to describe atomic orbitals, regions of space in which an electron can be found. From these numbers, we can determine the different properties of electrons in an atomic orbital. It is important to note that each electron will be unique to another, according to the Pauli Exclusion Principle. For this to be true, no two electrons in the same atom can have the same four quantum numbers.

The Principal Quantum Number (n)

The principal quantum number (n) describes the electron shell, or the size, of an orbital. An electron shell can be thought of as the part of an atom where an electron orbits the nucleus. Learn about how Rutherford discovered the nucleus.

The only allowable values of n are whole number integers starting from 1. A higher n value means that the associated electron is farther away from the nucleus. For example, an electron with n = 1 would be much closer to the nucleus than an electron with n = 5. When comparing electrons with the same l, we can also say that an electron with a higher n value is higher energy. With higher n, an electron will not feel the attractive pull of the positively-charged nucleus due to its farther distance. The electron’s negative charge is not stabilized, so the electron is higher energy.

Orbital Shapes – The Angular Momentum Quantum Number (l)

There are four different kinds of orbitals, which are named s, p, d and f orbitals. They each have a different orbital shape. An s-orbital is spherical with the nucleus at its center. A p-orbital is dumbbell-shaped and four out of five d-orbitals are cloverleaf shaped. The last d-orbital is an elongated dumbbell with a donut around its center.

The angular momentum quantum number (l) describes the subshell, or the shape, of an orbital, and its allowable range is (0, …, n – 1). There are four distinct shapes to remember: the s, p, d, and f orbitals. The value of l assigned to each subshell is based on the number of angular nodes (planes). For s orbitals, which are spheres, there is no angular node, so l = 0. For p orbitals, which has electron density separated by one angular node, l = 1. Following this trend, d orbitals would have l = 2 and f orbitals would have l = 3, as they have two and three angular nodes, respectively.

The Magnetic Quantum Number (ml)

The magnetic quantum number (ml) describes the various orientations of subshells in 3D space. Its range is (-l, …, l), meaning that for how many ways you can uniquely rotate a certain shape, you have that many possible ml values. Because there is not a new, distinct orientation when you rotate a sphere around the origin, the s orbital will only have one possible magnetic orientation. But due to the angular nodes of the p, d, and f orbitals, they have many possible ml values, as indicated in the diagram below.

The Spin Quantum Number (ms)

The spin quantum number (ms) describes the spin of a certain electron in an orbital. The spin is either +/- ½, which denotes either an up spin or a down spin. Each orbital can hold a max of two electrons, and if fully filled, the electrons cannot share the same spin direction. If electrons do not point in the opposite direction, then it would be a violation of the Pauli Exclusion Principle — two electrons cannot share the same four quantum numbers. If the orbital is not fully occupied, then the electron can take on any spin direction. Convention usually assigns the up spin first in a non-fully occupied orbital.

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