Atomic Orbitals and Quantum Numbers - Bonding - MCAT Organic Chemistry Review

MCAT Organic Chemistry Review


3.1 Atomic Orbitals and Quantum Numbers

Bonding occurs in the outermost electron shell of atoms, so an understanding of bonding is contingent on understanding the organization of electrons in an atom. Quantum numbers are discussed in detail in Chapter 1 of MCAT General Chemistry Review, and are briefly summarized here.

The first three quantum numbers, n, l, and ml, describe the size, shape, number, and orientation of atomic orbitals an element possesses. The principal quantum number, n, corresponds to the energy level of a given electron in an atom and is essentially a measure of size. The smaller the number, the closer the orbital is to the nucleus, and the lower its energy. The possible values of n range from 1 to ∞, although the MCAT only tests on n-values up to 7.


Recall from Chapter 1 of MCAT General Chemistry Review that quantum numbers describe the location of an electron within an atom and that each electron has a unique combination of quantum numbers according to the Pauli exclusion principle.

Within each electron shell, there can be several subshells. Subshells are described by the azimuthal quantum number, l, which ranges from 0 to n – 1 for a given energy shell. The l-values 0, 1, 2, and 3 correspond to the s, p, d, and f subshells, respectively. Just as with the principal quantum number, energy increases as the azimuthal quantum number increases.

Within each subshell, there may be several orbitals. Orbitals are described by the magnetic quantum number, ml, which ranges from –l to l for a given subshell. Each type of atomic orbital has a specific shape, which describes the probability of finding an electron in a given region of space. An s-orbital is spherical and symmetrical, centered around the nucleus. A p-orbital is composed of two lobes located symmetrically about the nucleus and contains a node—an area where the probability of finding an electron is zero—at the nucleus. Picture the p-orbital as a dumbbell that can be positioned in three different orientations, along the x-, y-, or z-axis. It should make sense that there are three p-orbitals; the p subshell has the l-value of 1, so there are three possible values for ml: –1, 0, and 1. The shapes of the first five s- and p-orbitals are shown in Figure 3.1. A d-orbital is composed of four symmetrical lobes and contains two nodes. Four of the d-orbitals are clover-shaped, and the fifth looks like a donut wrapped around the center of a p-orbital. Thankfully, the multiple complex shapes of d- and f-orbitals are rarely encountered in organic chemistry. Each orbital can hold two electrons, which are distinguished by the spin quantum number, ms. The only values of ms are

Figure 3.1. The First Five Atomic Orbitals

MCAT Concept Check 3.1:

Before you move on, assess your understanding of the material with this question.

1. Summarize the quantum numbers below. The first entry has been completed for clarification.