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. 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. Isotopes typically exhibit similar chemical behavior to each other.
Electrons have such little mass that they exhibit properties of both particles
and waves; in. We further 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 atomic
orbitals.
Atomic Orbitals and Quantum Numbers
The relation of a particular electron to the nucleus can be described through a
series of four numbers, called the Quantum Numbers. The first three of
these numbers describe the energy (Principle quantum number), shape (Angular
momentum quantum number), and orientation of the orbital (magnetic quantum
number). The fourth number represents the "spin" of the electron (spin quantum
number). The four quantum numbers are described below.
Principle Quantum Number (n)
The principle quantum number indicates how the distance of the orbital from the
nucleus. Electrons are farther away for higher values of n. Electrons are
negatively charged, so electrons that are closer to the positively charged
nucleus are more powerfully attracted and tightly bound than those that are
farther away. Electrons that are closer to the nucleus are thus more stable,
and less likely to be lost by the atom. In other words, as n increases,
so does the energy of the electron and the likelihood of that electron being
lost by the atom. 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)
The angular momentum quantum number describes the shape of the orbital. The
angular momentum number (or subshell) can be represented either by a number
(any integer from 0 up to n-1) or by a letter (s,p,d,f,g, and then up the alphabet), with 0 corresponding to
s, 1 to p, 2 to 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 s,p, 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. For example:
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
