00:01
Hi there.
00:02
In this question, we are working with scandium, which is atomic number 21.
00:09
So the first thing i want to do is write the electron configuration for scandium.
00:13
Since the atomic number is 21, and atom will have 21 electrons to match those 21 protons.
00:20
So the electron configuration, of course, begins with 1s2, and we have 2s2, followed by 2p6.
00:29
We have 3s2, 3p6, 4s2, and 3d1.
00:43
So this is the electron configuration with the electrons filling, according to alphbauer's rule, where they fill the lowest energy first.
00:51
So we want to write a set of quantum numbers for each of the electrons where the principal quantum number n is equal to three.
01:00
So that means the 3s2 electrons, the 3b, six electrons and this one electron in the 3d.
01:11
Those all have n equals three.
01:15
All right.
01:16
So that means there are four quantum numbers.
01:19
There's the principal quantum number, which tells you the energy level.
01:24
There is the angular momentum quantum number, which will tell you the shape of the orbital.
01:29
There's the magnetic quantum number, which tells you the orientation in space of the orbital.
01:34
And then the spin quantum number, which can be, either positive 1 half or negative 1 half.
01:41
So let's start with our two electrons in the 3s.
01:45
Principal quantum number for each of these electrons is three, because they're in the third energy level.
01:52
The angular momentum quantum number, since it's an s, is going to be zero.
01:58
When the angular momentum quantum number is zero, the shape is an s.
02:03
Since the angular momentum is zero, the only possible value for the magnetic quantum number is also zero, because the magnetic quantum number ranges from negative l to positive l, with l being the angular momentum.
02:21
Right, and then there are two electrons.
02:24
One of them has a positive one -half spin, the other has a negative one -half spin...