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Hi, my name is Jessica. I'm an SI leader for Chemistry 120, and today I'm going to talk
about quantum numbers on the periodic table. Today we're going to talk about quantum numbers
on the periodic table. It's easiest to think of these numbers as
GPS coordinates of each element on the periodic table.
There are four quantum numbers: n, l, m_l, and m_s. Let's start with n.
n tells us the energy level. In regards to the periodic table, this tells us the specific
row that we need to look at. Since there are 7 rows, 1, 2, 3, 4, 5, 6,
and 7, then n may have a value between 1 and 7.
If we have n=2, we must be talking about an element found within the second row.
l tells us the specific orbital. For this video, we'll call these the orbital sets.
There are four orbital sets on the periodic table: s, p, d, and f.
Therefore, there must be four l values. l starts at 0, and ends at 3. We always start
with s. So s must be equal to 0. p=1, d=2, and f=3.
So when we say l=3, we know that we must be talking about an element in the f orbital
set. m_l tells us the specific suborbital we are
referring to, and can have a value from -l to +l, and must include 0.
Remember from electron configuration that orbitals only fill one electron at a time
across a row, and then start at the beginning of the row again.
This means that each column within your orbital set has a specific orbital to fill, and the
number of orbitals is equal to the number of columns divided by 2.
Why 2? Because remember, each suborbital takes exactly 2 electrons.
So let's take oxygen, element number 8. This is n=2, l=+1. m_l=-1. Why? Take a look at
the columns. We have boroon, carbon, and nitrogen, and then three additional elements following.
Oxygen starts. Boron, carbon, and nitrogen make up the first three electrons to fill
the three orbitals of the p orbital set. Since there are six columns in the p orbital
set, there must be three orbitals. Boron is going to fill the -1 orbital, which is m_l=-1.
Carbon is going to fill the 0 orbital, m_l=0. Nitrogen is going to fill the 1 orbital, m_l=+1.
Because we have exactly three orbitals, and all orbitals can only take 2 electrons,
when we start over with oxygen, we must start over with -1. The next element would be 0,
and the final element, being the halogen, would be +1.
Let's look at all of our orbital sets. Starting with s, there is only one suborbital because
there are only two columns. So m_l must be 0 for the entire orbital set.
The p orbital has 6 electrons, which means 6 divided by 2 is equal to 3. Therefore the
values must be -1, 0, and +1, to repeat a second time across the columns.
The d orbital has 10 electrons, so 10 divided by 2 is going to be equal to 5 orbitals. Since
we need 5 m_l values, and they must include 0, the first m_l value must be -2, -1, 0,
+1, +2 and then repeats again. -2, -1, 0, +1, and +2 across the row. The
f orbital has 14 electrons. So 14 divided by 2 gives us 7 suborbitals.
Since we must have 7 values for m_l, including 0, the numbers must be, across the row, -3,
-2, -1, 0, +1, +2, and +3. And again repeats. -3, -2, -1, 0, +1, +2, and +3.
Now what about m_s? This is called the spin number, and refers to the specific electron
we're looking at. The first electron always has a positive spin,
so boron, carbon, and nitrogen would all have m_s values of +1/2. However, when we start
filling the second electron, we switch over to -1/2.
This means that oxygen's m_s value is equal to -1/2, as is fluorine, which would be right
next to it, and finally neon, which is the halogen along this row.
There are a couple of important rules to remember. The d orbital set always fills one row above
on the periodic table. So the element titanium, for instance, which
is Ti, is going to have quantum numbers of n=3, l=2, m_l=-1, m_s=+1/2.
Notice that n=3, even though if you just look at the periodic table, it looks like it should
be included on the fourth row. This is because the d orbital does fill starting
one above. The same can be said of the f orbital set. These start to fill on the fourth row
instead of the third. So, an element like plutonium has quantum
numbers n=5, l=3, m_l=+1, m_s=+1/2. Notice that n=5, not 7.
Hopefully this will help you to read the periodic table as a map using your quantum numbers.
Good luck!