Oh! Hello I didn’t see you there. Well because
you all look so excited to learn about quantum
mechanics I won’t stall anymore. We will
be continuing on from last lesson and we will
begin by talking about atomic orbitals. Heisenberg's
uncertainty principle stated that you cannot
know with certainty both the position and
velocity of an electron. An orbital is a region
of space where the electron is likely to be
located, this is also called a probability
distribution map. These orbitals are derived
by solving the Schrodinger's equation. Now,
don’t worry, you do not need to know how
to solve this equation but it is important
for you to know before we delve into the next
portion of this lesson. If you were to plot
a single electron, for example a hydrogen
atom, at a single position and you kept plotting
this electron at new positions the end result
would be a probability distribution map of
the electron. Which would be a 3D map of all
the places the electron could probably be
located. So as I mentioned, we will not be
going into the solutions of the Schrodinger
equation but instead we will be focusing on
the probability distribution maps or also
known as the orbitals. When talking about
the orbitals and characterizing them we will
go over 4 numbers which are known as quantum
numbers. 3 of these numbers are going to describe
the orbital it self and the fourth number
will describe the orientation of the electron.
Before we talk about these quantum numbers,
I want to first introduce an analogy that
will help you better understand quantum numbers.
So let's talk about an address for a moment
because each component of an address is vital
for giving a location of where a place or
someone is located at. If you had a meeting
for a job and the company only told you it
is in Orlando, FL could you locate where your
meeting was going to be? Well no you could
not the only thing you could identify is that
city it was in. Well the second thing they
give you is a zip code. Well that’s wonderful
because now you have identified a region in
the city where it could potential be. The
next piece of information that is provided
is the street name well that’s better but
still not great because you are still unsure
where the meeting is located. So all you are
missing is the street number because this
is the last piece to the puzzle that you needed
to identify where your meeting is at. So you
can probably assume at this point the quantum
numbers that we will be covering will be similar
in a way to characterize the orbitals and
probable location of the electron.
The first quantum number, which is denoted
by “n” and is called the principle quantum
number. The principal quantum corresponds
to the size and energy of the orbital and
can be equal to an integer that is greater
than or equal to 1. This quantum number is
the city. Because it is describing the energy
level in which the electron is located at
either closest to the nucleus (which would
be n=1) or further away which might be denoted
by 2,3,… etc. We have seen n before in an
earlier lecture do you remember? Yes this
is the same “n” from Bohr’s equation.
The second quantum number is the angular momentum
quantum number (denoted by l) which denotes
the shape of the orbital. This quantum number
is calculated by l=0 to n-1 including all
integers in between. Each calculated value
of l corresponds to a specific orbital shape.
When l=0 this is an s orbital, l=1 is a p
orbital, l=2 is a d orbital. It is important
to know which value of l corresponds to the
shape of the orbital. This quantum number
is like the zip code because now we are identifying
which orbital this electron can be located
at. The third quantum number is the magnetic
quantum number denoted by ml which determines
the orientation in space of the orbital, so
this denotes where on the XYZ plane this orbital
lies upon. IT IS EXTREMELY IMPORTANT TO NOTE
THAT EACH ORIENTATION OF AN ORBITAL CAN HOLD
A MAXIMUM OF 2 ELECTRONS. I will repeat that
again each orientation of an orbital can hold
a maximum of 2 electrons. So the magnetic
quantum number is like the street address
because we have now narrowed down the location
even further. In order to calculate ml it
is -L...0…+L. So for example if we have
l=2 so a d-orbital what are the allowed ml
values? Well, it would be -2,-1,0,1,2. How
many orientations does the d-orbital have?
Well it had a total of 5. So what is the maximum
number of electrons that can held in the d
orbital? That’s correct 10 e- and we could
do that for each value of l. Let's do another
one let's say we had a p-orbital so l=1, ml
would be -1,0,+1 so it has 3 different orientations
in space and could hold a max of 6e- because
each individual orientation can hold 2e-.
So those 3 quantum numbers described the orbitals
so the last quantum number represents spin
(ms) which specifies the orientation of the
electron in the orbital An electron could
be spin up, which is denoted by +1/2 or spin
down which is -1/2. These are the only values
that are allowed for spin. So in the previous
analogy the spin would represent the street
number.
So know that we understand each quantum number
lets go over a few pieces of information and
definitions. A shell is any orbital with the
same value “n” and a subshell are orbitals
with the same value of “n” and “l.”
So you must be thinking what do these orbitals
look like? Well let's start with the s orbital
which is the lowest energy orbital. This orbital
is a spherically symmetrical orbital. So going
back to the orientation of this orbital in
space, so ml. If I was to rotate it, would
you be able to tell that I did so? Well no
you wouldn’t because it is all symmetrical.
Also, for an S orbital, l=0 and ml= 0. elaborate
on each number
For the p-orbital (when l=1) we saw earlier
that it had 3 orientations in space (ml=-1,0,+1).
The p-orbital kinda looks like a peanut and
each lobe is a region of electron density
and if we were to rotate this there could
be 3 different orientations on the XYZ plane.
So you have the px which lies on the x-axis,
py, and pz .
The last orbital we will focus on is the d-orbital
which as we went over earlier has 5 orientations
in space and resembles a daisy. The orientations
are as followed: dxz, dyz, dxy, dx^2-y^2,
and dz^2 and if you combine them all together
you get dog… bumdumdachin I am kidding there
is no dog orbital.
So I know today's lesson was a little lengthier
than the ones previous but please make sure
you re-watch this lesson if you missed anything.
Please write down any questions you may have
so we can review it in lecture. Also watch
the corresponding worked out problems so you
can see how everything ties together. Have
a wonderful day and thanks for watching!
