Introduction to Quantum Mechanics

We're going to take a look at the quantum mechanical picture of the atom.
What we need to realize is that the main atomic sub-levels are s, p, d, and f. These are also sometimes referred to as sub-orbitals, but we're going to call them for right now, sub-levels, s, p, d, and f. We're going to say each sub-level has a set of atomic or electronic orbitals and what I mean by that are these individual lines. Each of these individual lines represents an electron orbital or atomic orbital. We're going to say each of these orbitals, electron orbitals, can hold up to two electrons. 

The s sub-level has one electron orbital, therefore, s can hold a maximum of two electrons. The p sublevel has three electron orbitals, each one can hold up to two, so we have six maximum in the p sublevel.
Also remember that each one of these sub-levels has a shape distinct to them. In s, we only have one electron orbital, so we only have one shape and it's a sphere.
For p, p has three electron orbitals each of them has their own shape. P has three dumbbells. And these dumbbells reside on different axes. Here, this would be px because it resides on the x-axis. This would be py because it resides on the y. Then these would be pz because they reside on the z-axis.
We're going to say that the d sublevel has five electron orbitals, each one can hold two, so the d sublevel can hold a maximum of ten electrons. We're going to say that in the d we're going to have four, four-leaf clovers, so these first four are all four-leaf clovers. And then the last one, the fifth one, looks like a dumbbell with a ring around it. Remember these shapes. These shapes are distinct.
Then finally, we're going to say that the f sub-level has 7 electron orbitals, seven unique shapes. And then we're going to say because it has seven electron orbitals, it can hold a maximum of 14 electrons. We're going to say that for the f sub-level, three of them kind of look like this. Then we're going to say four of them look like double four-leaf clovers.
These shapes are going to become important for later on when we're asked questions just based on these shape of sub-levels. Just remember, we have four sub-levels, s, p, d, and d. There's more than just these four, but these are the main four that we deal with on a typical basis in quantum mechanical views in chemistry. There's four sub-levels, each sub-level has a different number of electron orbitals, each electron orbital can hold up to two electrons.
Remember these fundamentals because from here we're going to move on to the quantum numbers. The quantum numbers are based on these simple ideas which help build up to more complex ones later on.

In the next video, we are going to cover a topic that is incredibly important when it comes to these sets of videos. It’s all about the quantum numbers. Now, we are going to say when it comes to an atomic orbital or an electron orbital we talk about three quantum numbers. Now, the thing is there are four quantum numbers, it just happens to be that the first three only talk about the atomic orbital. The fourth quantum number doesn’t talk about the atomic orbital at all; it talks about the spin of the electron. So that’s why we are not talking about the fourth quantum number just yet.
Now we are going to say the first quantum number is referred to as the Principal Quantum number and it deals with the atomic orbital’s size and energy. It tells us the relative distance of the electron from the nucleus. We are going to say it uses the variable n and it tells us the shell number of the electron.
We’ve seen this before where we see n equals four or n equals two. We said that told us that the electron was found in the fourth shell or the second shell. Well, we should realize that it’s related to our Principal Quantum number. It basically tells us how far away we are from the nucleus and basically how much energy and size is involved with those particular electrons.

Now for the first example, it says calculate the principal quantum number of each atomic sub-level.
It sounds complicated but it’s really easy. We are going to say that the principal quantum number is just based on the number that goes in front of the sub-level letter. So in the first one (a) 7p, the number that is in front of p is a 7. So all we would say here is that n equals 7. It’s as simple as that. For (b) 5s, the number in front of s is a 5, so n equals 5. For (c) it would be n equals 3, and for (d) it would be n equals 4.
Just remember the number that goes in front of the sub-level letter represents our principal quantum number. It’s as easy as that.
Now we are going to say that the electron capacity of each shell can be determined by using the formula: 2n squared. Where n represents the shell number. So if we are in the first shell we can figure out how many electrons the first shell holds by using this formula. It would just be 2 times 1 squared. So that would just be 2. If we are in the second shell it would be 2 times two squared. So that would be 2 times 4 which would be 8. So the second shell can hold a maximum of 8 electrons. For the third shell, it would be 2 times 3 squared. So it would be 2 times 9, so that would be 18. And then finally four, it would be 2 time 4 squared which is 2 times 16, which is 32.
Now we are going to say that I only went up to four but there is more than four shells, electron shells. The number of shells is based on the number of periods of the periodic table. If you guys remember we say that groups go vertical, up and down right? Side to side, those are our periods. On our periodic table, there are seven periods. So that means we go up to shell number seven when it comes to elements.
And, the more and more elements we discover or create in the lab the more periods we are going to add to the periodic table. The periodic table is not static; it is always changing, ever evolving and getting bigger and bigger. So eventually it’s going to come to a point where we are going to go beyond shell number seven to shell number eight, shell number nine; who knows. It all depends on how far we are willing to push, find, and create new elements.
Now just remember period number is a reflection of the electron shell number. So that was our first quantum number principal.

The next one is called our angular momentum quantum number. This one deals with the shape. So remember this one deals with the shape of the atomic orbital. Remember all those shapes that I had you memorize for s, p, d and f, those shapes are determined by this quantum number, the angular momentum quantum number.
And we are going to say each atomic orbital has a specific shape, which we just said, and we say that the variable for the angular momentum quantum number is L, and we are also going to say that it also uses the formula n minus 1. And we will see when do we use the L value and when do we use the n minus 1 value.
Now if we know the sub-level letter we know what the L value is. So, if the sub-level is s then L is 0. If it’s p, it’s 1, d it’s 2, f it’s 3. Remember I told you that there’s more than just those four sub-levels, it goes beyond f. We have g, we also have h. Usually you don’t see g and h, but just realize that those exist as well. And, each of them, if you know the sub-level letter, then you know what the L value is.
Now, if we don’t know what the sub-level letter that’s when we use this formula: n minus 1. We will see who that works when we put to practice calculating things and dealing with the quantum numbers.
So, so far we’ve done the principal, now we’ve just done the angular momentum. If we come back up we could figure out what the L value is for each of these because we are going to say that the number designates our n value, but the letter, the sub-level letter designates our L value. So if it’s p, L is 1. If it’s s, L is 0. If it’s d, L is 2. If it’s f, L is 3.
So far we know the first two quantum numbers. Now it’s time to take a look at the third one. 

We are going to say that the third quantum number is known as the magnetic quantum number and this deals with the orientation of the orbital in space around the nucleus. We are going to say it is a range of the previous quantum number -l to +l. We will see what that means. And, we are going to say that it uses the variable ML.
Now here I said if we know what the sub-level letter is then we know what the L value is. We are going to say that our magnetic quantum number our ML is just the range of our L. What the heck does that mean? Well, if L is zero is there such a thing as positive and negative zero? You realize that there isn’t, right? There is no such thing as positive zero or negative zero. Zero is just zero. So ML would be zero as well.
But, when L is one, remember there is such a thing as positive one or negative one. So, ML would be negative one to positive one and all the whole number in between. So it would be negative one, zero, positive one. If L is two then ML is negative two to positive two and all the whole numbers in between. So the range would be negative two, negative one, zero, plus one, plus two. And then if we go here, ML would be negative three, negative two, negative one, zero, plus one, plus two, plus three.
I am going to take myself out because we are going to talk about one more thing guys.
Now how many electron orbitals does the s have? If you guys remember, it has one, right? There it goes right there. How many electron orbitals does p have? It has three. How many electron orbitals does the d have? It had five. And, how many electron orbitals does the f have? F has seven.
And, you’ll see that I just underlined each one of these numbers because each of those numbers is actually a label for each one of those electron orbitals. It’s a way of describing which electron orbital are we talking about within each sub-level. So, p has three electron orbitals that’s why it can hold up to six electrons. This electron orbital will be negative one as its designation, this would be zero, this would be positive one. D, d has five electron orbitals, and we’d say that this one would be called negative two, this one would be called negative one, this one would be zero, plus one, plus two.
So remember that image that we looked at, that page where it talked about the quantum mechanical picture of the atom. Just put these numbers underneath each one of those electron orbitals. That’s a way of us labeling and identifying each one of those individual electron orbitals based on their sub-level.
So, as you can see the quantum numbers are not just simply separated from each other; they build on top of each other. They are connected to one another, and the more problems we do together you’ll see these connections. Quantum mechanics and quantum numbers can be a bit challenging, but just remember these fundamental principles and it will help you to better understand this advanced topic.