Quantum mechanics gave us a way to accurately
calculate the probability of where an electron
was in an atom using wave. It turns out that
Heisenberg's Uncertainty Principle allowed
us to either calculate the specific location
of an electron or to know the energy of the
wave but we couldn't do the both at the same
time. Quantum mechanics uses the wave notion
to accurately predict the behavior of elements.
The loss of this is that we only got a probability
of where an electron was. We can give an address
to this probability by using quantum numbers,
best way to think about quantum numbers is
it's kind of like an address for us. You would
be in a country, a state, town, street, and
then your street address and that would give
us a probability of where we might be able
to find you. You may or may not be there but
it would give us a probability. So when we
think about electron densities and quantum
numbers that's what we're getting with quantum
mechanics. There are four quantum numbers:
the principal quantum number, the angular
momentum quantum number, the magnetic quantum
number, and the electron spin quantum number.
These are given by n, l, m sub l and m sub
s; n is our basic energy levels. If we think
about it we can think about it as size and
they correlate very well to the Bohr model.
They're integers 1, 2, 3, 4 and so forth.
l is defined by n-1. If n is zero then l can
only be zero. If n is one then l has to be
zero. If n is two then l can be one and zero.
Our next quantum number is m sub l as you
might determine from the fact that it's m
sub l it's going to be defined by l; m sub
l is our orientation. It's usually given by
minus l as whole integers down to zero and
then past zero up to plus l. If we take l
equals one that means that our orientations
for m sub l will be -1, 0, and +1. Our last
quantum number m sub s is the electron spin
quantum number. It really only has two possible
values -1/2 and +1/2 . When we look at all
this together it gives us the probable location
of electron based on the electron density
map that we calculated by quantum mechanics.
Let's take an example. Let's take n equals
2. So we're gonna look at an element that
has a energy level at least two. From that
that will give us two possible l or shapes.
Those shapes will be zero and one. If we think
about the m sub l for example where l is zero
and one the m sub l for l equals zero is zero.
There's only gonna be one orientation. If
we look at the m sub l where l equals one
we're going to have three orientations: minus
one, zero, and one. If we think about this
in three dimensions these can be along our
access x, y, and z. Now for each of these
orientations we're gonna have two possible
m sub s. We will have the -1/2 and the +1/2.
If we put these altogether this will give
us a probable location for our electron. We're
gonna combine these to give the electron configurations.
One more piece of information when we looked
at our l zero, one, two, and three they had
specific shapes. The shape for zero was s.
Zero actually gives us some very important
information about the shape there are no nodes
in this three-dimensional shape. For l equals
one that's referred to as p or the p-shape.
Since l equals one it has one node so all
the shapes in p will have one node. When we
look at l equals 2 we refer to that as d it's
going to have two nodes and when we look at
l equals three that is f and it'll have three
nodes. All of the quantum numbers give us
probable electron densities and locations
for our electrons. We're gonna be able to
use these along with electron configurations
and the periodic table to help us predict
the reactivity and the physical properties
of the elements.
