Final Quantum Number Post
Dec. 13th, 2008 11:08 pm![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
tanarillOkay, so. Principal and angular quantum numbers are down. Next is the magnetic quantum number, which gets an "m". The reason it is called magnetic has to do with what happens to electrons beams if you put the atoms in a magnetic field, and is not terribly important. First, though, I shall connect the possible l values to orbitals.
If l=0, you get spherical or "s" orbitals. If l=1, you get stretched-infinity or "p" orbitals. If l=2, you get "d" orbitals. And if l=3, then you get "f" orbitals. As you can see, from any given l, there's more that one possible orbital. Orbitals that have the same n but different l are also called "subshells."
m tells you how many possible orbitals there are. m can be -l to l, by whole numbers. So if l=0, then m is also 0, but if l=2, then m can be -2, -1, 0, 1, and 2. If you look at this, it generates five possible orbitals.
Orbitals are not mutually exclusive. Let me repeat that. More than one orbital can be in the same place at the same time. In fact, not just orbitals of the same l, but orbitals of different l and difference n can be in the same place and the same time.
An example. There is an atom of n=3. Then all possible orbitals are:
n=1, l=0, m=0
n=2, l=0, m=0
n=2, l=1, m=-1
n=2, l=1, m=-0
n=2, l=1, m=1
n=3, l=0, m=0
n=3, l=l, m=-1
n=3, l=1, m=0
n=3, l=1, m=-1
n=3, l=2, m=-2
n=3, l=2, m=-1
n=3, l=2, m=0
n=3, l=2, m=1
n=3, l=2, m=2
for a grand total of fourteen orbitals. All of these orbitals can exist in the same space at the same time. The actual electrons can't be in the same place and the same time, but they hate each other anyway and repel each other before they hit. So in this model, there are three s orbitals, six p orbitals, and five d orbitals.
Each orbital can hold up to two electrons, for a total of twenty-eight possible electrons. Yes, I know electrons hate each other. But they will drop into an orbital with another electron rather than having higher energy.
The orbitals are not all always filled. In the neutral state, an atom will have exactly as many electrons as it has protons. In ionized states, they'll have either more of fewer electrons. How many they gain or loose usually has to do with filling or emptying a subshell. Atoms like subshells to be either totally empty, exactly half-full, or totally full, for reasons I'm not going to explain right here.
That's not all there is to orbitals and subshells, but it is all you need to know when you are not dealing with atomic stability, or bonding. If you want, I will explain more but it's not really helpful for anything other than being a chemist.
Hm. That was short. I will explain spin, which gets "s". This is not the same "s" as in the s orbital.
Electrons hate each other. Even though they will drop into the same orbital to loose energy, they don't like it.
Electrons do, however, have this thing called spin. Pretend that they are like tiny little planets. They're spinning on an axis. They are either spinning to the right (like the earth) or to the left. When they are spinning to the right, we say they are spinning "up" and have s=1/2. If the are spinning the left, we say they are spinning "down" and have spin s=-1/2.
Two electrons in the same orbital always have opposite spins. If an electron of the same spin falls into an orbital, on of the electrons flips over to change it's spin without actually stopping and then starting in the other direction. The opposite spins cause very tiny opposing magnetic fields, which attract, and allow them to coexist.
This leads to the final point about electrons in orbitals. No two electrons around the same atom can have all four quantum numbers the same. It does not work. Each electron can be described with a different four numbers.
And that's all about orbitals, or at least all you need to know not being a particle physicist. If there was something you didn't get or want to know that I didn't go over, just ask and I will try to explain better.
That is all for Science! Now to go off and write this Haunted Past . . .
If l=0, you get spherical or "s" orbitals. If l=1, you get stretched-infinity or "p" orbitals. If l=2, you get "d" orbitals. And if l=3, then you get "f" orbitals. As you can see, from any given l, there's more that one possible orbital. Orbitals that have the same n but different l are also called "subshells."
m tells you how many possible orbitals there are. m can be -l to l, by whole numbers. So if l=0, then m is also 0, but if l=2, then m can be -2, -1, 0, 1, and 2. If you look at this, it generates five possible orbitals.
Orbitals are not mutually exclusive. Let me repeat that. More than one orbital can be in the same place at the same time. In fact, not just orbitals of the same l, but orbitals of different l and difference n can be in the same place and the same time.
An example. There is an atom of n=3. Then all possible orbitals are:
n=1, l=0, m=0
n=2, l=0, m=0
n=2, l=1, m=-1
n=2, l=1, m=-0
n=2, l=1, m=1
n=3, l=0, m=0
n=3, l=l, m=-1
n=3, l=1, m=0
n=3, l=1, m=-1
n=3, l=2, m=-2
n=3, l=2, m=-1
n=3, l=2, m=0
n=3, l=2, m=1
n=3, l=2, m=2
for a grand total of fourteen orbitals. All of these orbitals can exist in the same space at the same time. The actual electrons can't be in the same place and the same time, but they hate each other anyway and repel each other before they hit. So in this model, there are three s orbitals, six p orbitals, and five d orbitals.
Each orbital can hold up to two electrons, for a total of twenty-eight possible electrons. Yes, I know electrons hate each other. But they will drop into an orbital with another electron rather than having higher energy.
The orbitals are not all always filled. In the neutral state, an atom will have exactly as many electrons as it has protons. In ionized states, they'll have either more of fewer electrons. How many they gain or loose usually has to do with filling or emptying a subshell. Atoms like subshells to be either totally empty, exactly half-full, or totally full, for reasons I'm not going to explain right here.
That's not all there is to orbitals and subshells, but it is all you need to know when you are not dealing with atomic stability, or bonding. If you want, I will explain more but it's not really helpful for anything other than being a chemist.
Hm. That was short. I will explain spin, which gets "s". This is not the same "s" as in the s orbital.
Electrons hate each other. Even though they will drop into the same orbital to loose energy, they don't like it.
Electrons do, however, have this thing called spin. Pretend that they are like tiny little planets. They're spinning on an axis. They are either spinning to the right (like the earth) or to the left. When they are spinning to the right, we say they are spinning "up" and have s=1/2. If the are spinning the left, we say they are spinning "down" and have spin s=-1/2.
Two electrons in the same orbital always have opposite spins. If an electron of the same spin falls into an orbital, on of the electrons flips over to change it's spin without actually stopping and then starting in the other direction. The opposite spins cause very tiny opposing magnetic fields, which attract, and allow them to coexist.
This leads to the final point about electrons in orbitals. No two electrons around the same atom can have all four quantum numbers the same. It does not work. Each electron can be described with a different four numbers.
And that's all about orbitals, or at least all you need to know not being a particle physicist. If there was something you didn't get or want to know that I didn't go over, just ask and I will try to explain better.
That is all for Science! Now to go off and write this Haunted Past . . .
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no subject
Date: 2008-12-15 12:43 am (UTC)I only have two questions:
1. In the example, if n=3, how come it can also have orbitals with n=2 and n=1. (Sorry if you already went through the reason, but I can't find it in the two previous posts.)
2. So, there is no way to tell how many electrons will be in a subshell, other than there have to be either 0, 1 or 2, and that the orbitals that are closer to the nucleus are more likely to be full than the ones that are farther? (...That question made sense, right? I get the feeling that I messed up the grammar in there.)
Actually, if you have the time to spare, I'd like for you to explain to me about bonds and ions. I knew about covalent, ionic, metallic, etc., bonds, but I never understood the reasons behind them (having been stumped in the subject you just taught me had a big part to do with it).
no subject
Date: 2008-12-15 01:42 am (UTC)1. The n you are told is just the highest principal quantum number in the atom; all the lower ones are there too. With only a few exceptions, the lower n must be filled completely before the higher n start filling up.
2. (Well, I understood it.) Yes, pretty much. Most of the time it's really not hard to figure out, though, because you will know from ionization or bonding how many electrons are around the atom. From there you just start filling the shells from the inside out until you run out electrons.
Okay, I will explain that, but you must wait a week. I have final exams this week and I want to get good grades. But never fear, and explanation is . . . on the way :P
no subject
Date: 2008-12-15 03:36 am (UTC)Yay! Thank you so much. I don't mind waiting. Good luck with your exams!