Leah here from Leah4sci.com/mcat and in this video we'll continue our discussion of Quantum
numbers as it'll show up on your MCAT. You can also follow along with my Cheat Sheets
which you can download on my website at leah4sci.com/mcatchemistry. In the last video we compared the concept
of Quantum numbers to a college dorm and we also introduce the four principal quantum
numbers that you have to know using the pneumonic PAMS. So now let's break it down into great
details. P stands for Principle energy level and is
designated by the letter n. This has to do with which level on the Periodic Table you
will find that specific electron. So if we look at the periodic table starting in Hydrogen
we have Na plus one and then going down we have two, three, four , five, six and seven.
But just because the table ends at seven doesn't mean our values end at seven. Because if you
have an electron and you give it a boost of energy, putting it into an excited state,
that electron can fill an orbital beyond level 7. And so your n value will be all positive
numbers starting from 1 and going to infinity. We'll use the formula 2n^2 to find out the
maximum number of electrons that you can have within a given principle level. For example,
when n is equal to 1, we have 2 times 1 squared. One squared is one, times two is two, that
means we have a maximum of two electrons. Take a look at the periodic table. At level
n equals one we have the hydrogen and helium. When you look at the atoms on the periodic
table, the electron configuration from one to the next is simply the atom in question
plus one electron. So Helium in terms of its electron configuration is just hydrogen plus
an electron. Lithium is just helium plus an electron. If you're not comfortable with this,
go back to my beginner Organic Chemistry videos where I break down electron configuration
and this concept. And you can find that on my website at leah4sci.com/OrganicChemistry.
But the way we want to look it here is that the table represents all the different possibilities
for the placement of an electron. So we said that when N is equal to 1 we have a maximum
of 2 electrons with the outermost electron of the hydrogen and helium that verifies the
presence of just the two electrons. If we try 2n^2 for n equals 2, that means
we have two times to two squared. With 2 squared is four times two is eight so at the second
principle energy level, we expect to have a maximum of eight electrons and if we can
count 8 atoms we know we're good. One, two, three, four, five, six, seven, eight. When
it comes to three it gets a little bit harder to see but let me show you anyway.
If we have two n squared (2n^2) and n is equal to 3, we have 3 squared is 9 times 2 is 18
but if you count the atoms at Principle energy level 3, it looks like once again we only
have 8. Two in the S area, six in the P area. But don't forget that the 3D orbital is higher
in energy than the 4s so after you fill 4s, this area is actually 3d and that means with
3d 1, 2, 3, 4 and so on in the electron configuration. When we count the 3d, we can't forget those
electrons and that means we have two, ten and six for a total of eighteen electrons.
The next quantum number to look at is A for Azimuthal Quantum Number and this is designated
by a lower case l. The l represents the orbital in which the electron is found and on the
MCAT you only have to know the s, p, d and f orbitals.
Mathematically the range for the Azimuthal number is from zero all the way to n minus
1. When n equals one, n minus one for one minus one is zero and that means we only have
we only have the zero orbital which is the s orbital. When n equals 2, n minus one two
minus one is one and that means we have zero and one or s n p.
When n equals three, n minus one is three minus 1 or two we have zero one and two or
S P and D. And finally when l equals 3, we have f. We'll use the formula 4l + 2 to determine
the maximum number of electrons within a specific orbital. So for example, if l is equal to
zero we already said that's the s orbital in which we have a maximum of two electrons.
Let's see how that works out. We have four times zero which is zero plus
two equals two and as we predicted the s orbital only holds two electrons. We know that p holds
six so let's prove that. Four l plus two, p has a value of one so we have four times
one plus two, that's four plus two is six and the p orbital does have six electrons.
Now let's see how you combine them. So for example, at the level n is equals three,
we have values for l of zero one and two and that's because n minus one is two, that gives
us s, p and d orbital. Let's see how the Math adds up, we have two n squared where n is
equal to three and that means two times three squared, 3 squared is nine times two is eighteen.
Let's see how we get those eighteen electrons. If we have 4l plus two for the S orbital,
this term is zero and that means we have two electrons. If we have 4l plus two for the
P orbital where l is equal to one, we have four times one plus four plus two equals six
electrons. And finally we have 4l plus two where l is two for d, that's four times two
is eight plus two is ten. Two plus six is eight, plus ten is eighteen and that's eighteen
electrons we predicted from 2n squared (2n^2). Remember this is the maximum number of electrons
but you don't always have a complete shell. The next value we want to look at is M which
stands for the Magnetic Quantum Number designated by M sub l, think of m sub l as the sub orbital
of l. in the S orbital you don't have any sub orbitals. Remember in the last video we
set as studio apartment doesn't have individual rooms but the P orbital is broken into three
orbitals. We have PX, PY and PZ and that would be the m sub l designations within the l value
so l is p m z that would be PXPY MPZ. Mathematically we can calculate m sub l and
from negative l through positive l and don't forget to have these zero inbetweeen. Since
s is zero, negative zero to positive zero is still zero but p being one we have negative
one zero and positive one that's how we get out three sub orbitals for P or XY and Z.
For D we have negative two negative one zero, positive one and positive two for a total
of five sub orbitals and so on. Now eventhough you have multiple sub orbitals they don't
necessarily have to go on order so don't worry about which one represents the negative one
or the zero or the positive one, just recognize the total value that you have and that when
they fill each one gets one electron until all of them have one then you back fill the
second one in two each. The final quantum number S which stands for
Spin is designated by the m sub s. in our apartment example we said we have the A portion
of the room and the B portion of the room. But in quantum numbers we designate this as
a positive one half or a negative one half. Every sub orbital can hold up to two electrons
and they'll have opposite spins that cancel each other out so we'll have the up spin and
the down spin. Which is which doesn't matter because we're
not calculating this at a Physics Mathematical level, we're simply understanding that there
are two types of electrons. What you do want to know is that if you have multiple sub orbitals
that are each half-filled and all their spins are align so for example you have one electron
each in PX, PY and PZ or at m sub s equals positive a half, these are said to be parallel
electrons. We'll discuss one final topic here and that
is the shape of the Orbitals. For the MCAT you're not expected to know the complex mathematical
shapes but recognize that the S orbital is a simple sphere with the center of the orbital
is the location of the nucleus , the orbital itself is the location of the electron but
it's constantly moving around and the farther way you go from the orbital the less likely
you are to find an electron there. For the p orbital we have the figure eight
or infinity symbol and we have three of them. PX in the X-direction, PY in the Y-direction
and PZ is coming half forward and half back. So we'll show the forward with a dark bold
orbital. I will show the back with a dotted orbital like it's fading into space. If you
want to put it all together you have PX, PY and there's your PZ.
Remember you can find this entire series along with the Cheat Sheets on How to Calculate
Quantum Numbers on my website at leah4sci.com/MCATChemistry. Are you overwhelmed by the sheer volume of
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