1. Atomic Structure

Atoms and Atomic Orbitals

This chapter is intended as a review of concepts covered in more depth in general chemistry from the organic chemist’s point of view. Bear in mind that many of the topics here are emphasized with an organic bent.

Fundamentals of the Atom

An atom consists of a nucleus of protons and neutrons surrounded by electrons. Each of the elements in the periodic table is classified according to its atomic number, which is the number of protons in that element’s nucleus. Protons have a charge of +1, electrons have a charge of -1, and neutrons have no charge. Electrically, neutral atoms have the same number of electrons and protons, but they can have a varying number of neutrons. Within a given element, atoms with different numbers of neutrons are isotopes of that element. We will see that isotopes typically exhibit similar chemical behavior to each other.

Electrons have such little mass that they exhibit properties of both particles and waves. We know from Heisenberg’s Uncertainty Principle that it is impossible to know the precise location of an electron. Despite this limitation, there are regions around the atom where the electron has a high probability of being found. Such regions are referred to as orbitals.

Atomic Orbitals

For isolated atoms (meaning non-bonded), electrons reside in the atomic orbitals of those atoms. Atomic orbitals are classified according to a set of four quantum numbers which describe the energy, shape, and orientation of the orbital.

Principle Quantum Number (n): Indicates how far the orbital is from the nucleus. Electrons are farther away for higher values of n. By Coulomb’s Law we know that electrons which are closer to the positively charged nucleus are more powerfully attracted and thus have lower potential energies. Electrons of orbitals with higher values of n, being farther away from the nucleus, have greater potential energies. In a given atom, all the atomic orbitals with the same n are collectively known as a shell. n can take on integer values of 1 or higher (ex. 1, 2, 3, etc.).

Angular Momentum Quantum Number (l): Describes the shape of the orbital. The angular momentum number (or subshell) can be represented either by number (any integer from 0 up n-1) or by a letter (spdfg, and then up the alphabet), with 0 = s, 1 = p, 2 = d, and so on. For example:

when n = 1, l can only equal 0; meaning that shell n = 1 has only an s orbital (l = 0).

when n = 3, l can equal 0, 1, or 2; meaning that shell n = 3 has sp, and d orbitals.

s orbitals are spherical, whereas p orbitals are dumbbell-shaped. d orbitals and beyond are much harder to visually represent.

Figure %: s and p atomic orbital shapes

Magnetic Quantum Number (m): Gives the orientation of the orbital in space; in other words, the value of m describes whether an orbital lies along the x-, y-, or z-axis on a three-dimensional graph, with the nucleus of the atom at the origin. m can take on any value from –l to l. For our purposes, it is only important that this quantum number tells us that for each value of n there may be up to one s-orbital, three p-orbitals, five d– orbitals, and so on: The s orbital (l = 0) has one orbital, since m can only equal 0. That orbital is spherically symmetrical about the nucleus.

Figure %: s orbital

The p orbital (l = 1) has three orbitals, since m = -1, 0, and 1. These three orbitals lie along the x-, y-, and z-axes.

Figure %: p orbitals

The d orbital (l = 2) has five orbitals, since m = -2, -1, 0, 1, and 2. It is far more difficult to describe the orientation of d orbitals, as you can see:

Figure %: d orbitals

Spin Quantum Number (s): Tells whether a given electron is spin up (+1/2) or spin down (-1/2). Because the Pauli Exclusion Principle tells us that no two electrons of an atom can have the same set of quantum numbers, each orbital is limited to holding two electrons at most.

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