Lets look back on what we discussed Friday.
As we discussed, quantum numbers are a method to pinpointing the probable location of a specific electron. Remember that my analogy, useful or not, likened quantum numbers to the address label on an envelope. Both increase in level of specificity until an exact location is pinpointed. With quantum numbers, there are 4 locations used to pinpoint the electron. Going from most general to most specific, they would be listed n, l, m, and s. So, lets look back at some rules governing how we use these.
n:
(n) applies to the principle energy level. In simplest terms, n corresponds with the period in which you're working. For example, if we were to look at Titanium, the period in which it is found would be period 4, so n would equal 4. For Zirconium, the period is 5, so n=5. So on and So on. Using n, we can find the general roaming grounds of an electron, but we're nowhere near its exact location. For that, we must find l.
l:
(l) represents the orbital in which an electron can be found. This is also very simple as long as you remember the following chart.
s=0
p=1
d=2
f=3
This can narrow our search, but as we discussed Friday, there are many "configurations" that the electron can be found in. We showed these configurations by drawing and labeling slots. These slots lead into determining (m).
m:
(m) is the most difficult to find, but if you remember how to label correctly and how to place electrons in orbitals correctly, you will have it made. First, you must remember that each orbital has a different number of ways that electrons can move around the nucleus. s has only 1 while p=3, d=5, and f=7. To determine in which configuration you can find an electron, you must first have a method of labeling each of those configurations. So what we do first is draw a slot for each configuration. Then we take the (l) we determined earlier and place that number under the far right slot. At this point, all you need to be able to do is count. Move from the far right to the far left decreasing by one integer with each slot. For example, lets continue to use Titanium. We know that it is found in the d-orbital, so (l)=2. Now we draw out the number of configurations that can be taken, which is 5. This is what it would look like.
_ _ _ _ _ next, we must label them by placing (l) at the far right and moving leftwards.
-2 -1 0 1 2
You MUST remember that one electron must be in each slot before any can pair. This means that all 5 slots will have a single ↑ in each before you will see any with ↑↓. Knowing this, we can see that Titanium will have an m value of -1 because it has two electrons in the d orbital, the last of which is located in the second slot ↑. If we were to look at Cobalt, it would also have an m value of -1 because it too has its outer electron in the second slot, but it would look like ↑↓. Finally, we must look at S.
S:
S represents the spin of the electron. Fortunately for us, there are only 2 ways an electron can spin. To denote this we use +1/2(↑)and -1/2(↓). It's that simple. Back to our example. Titanium's outer electron is located in the -1 orbital and since it is the first, it is written as an ↑. For this reason we apply an s value of +1/2 to it. Now look at Cobalt, we know that at this point, electrons have started pairing. We know that the outer electron is also located in the -1 orbital, but it is paired and looks like this ↑↓. Seeing that it points downward, we can apply an s value of -1/2 to it.
To wrap up, lets look at a couple of elements and determine their quantum numbers.
Titanium: n=4, l=2, m=-1, s=1/2
Cobalt: n=4, l=2, m=-1, s=-1/2
Zirconium: n=5, l=2, m=-1, s=1/2
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