Can someone explain how you calculate the energy levels (or the n,l,ml,ms) I'm very confused on how you can calculate and validate them.
Thanks
Electron Energy Levels
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Christopher Liu 3J
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Re: Electron Energy Levels
Are you talking about quantum numbers (n,l,ml,ms) or are you just talking about energy levels (specifically hydrogen's electron being excited to a certain n value)? I assume you mean quantum numbers.
Quantum numbers are like a unique tag for each electron; no two electrons in an atom can have the same set of quantum numbers. Let's use aluminum as our example.
n refers to principle quantum number. It is the shell the electron is located in. The period (aka row) determines what the highest n value you can have for an electron. In Al, it lies in period 3 so the highest n value is 3. Because atoms are like onions, electrons in Al can also have the n value 1 and 2, but it is most important to know that the highest is 3.
l refers to angular quantum number. This describes the shape subshells (e.g. 2p, 3s) can take on. All we need to know for now is determining what values of l are possible given an n value. l values can range from 0 to n-1. With n=3, l can take on the numbers 0,1,2.
l=0 refers to s
l=1 refers to p
l=2 refers to d
l=3 refers to f
l=4 refers to g
It keeps going but that's probably the highest we'll ever go.
ml is the magnetic quantum number, which labels different orbitals within a subshell (i.e. the orientation of an orbital). Allowed ml range from l, l-1,..., -l. So if given l=1, ml=-1,0,1. These just essentially name the orbital someone is trying to refer to. In l=1, because there are three orbitals, they can sometimes be labelled as the subscripts x,y,z after the subshell.
If someone refers to an electron in n=3, l=1, and ml=-1, that electron is in the orbital 3px.
ms is the magnetic spin quantum number. This one specifies the rotation of the electron in an orbital. In one orbital, there are two electrons at max and they must have different spin values. ms=-1/2 refers to an electron spinning down and ms=+1/2 refers to an electron spinning up.
And that's it for quantum numbers. So far, questions we've been asked before with quantum numbers is if a given set of QN values exist or not. For example, if the question gives n=1 and l=2, you know something is off because n=1 cannot have l=2. Some questions will also ask you to name the orbital given a set of quantum numbers, which I've already given an example of when talking about magnetic quantum number.
Quantum numbers are like a unique tag for each electron; no two electrons in an atom can have the same set of quantum numbers. Let's use aluminum as our example.
n refers to principle quantum number. It is the shell the electron is located in. The period (aka row) determines what the highest n value you can have for an electron. In Al, it lies in period 3 so the highest n value is 3. Because atoms are like onions, electrons in Al can also have the n value 1 and 2, but it is most important to know that the highest is 3.
l refers to angular quantum number. This describes the shape subshells (e.g. 2p, 3s) can take on. All we need to know for now is determining what values of l are possible given an n value. l values can range from 0 to n-1. With n=3, l can take on the numbers 0,1,2.
l=0 refers to s
l=1 refers to p
l=2 refers to d
l=3 refers to f
l=4 refers to g
It keeps going but that's probably the highest we'll ever go.
ml is the magnetic quantum number, which labels different orbitals within a subshell (i.e. the orientation of an orbital). Allowed ml range from l, l-1,..., -l. So if given l=1, ml=-1,0,1. These just essentially name the orbital someone is trying to refer to. In l=1, because there are three orbitals, they can sometimes be labelled as the subscripts x,y,z after the subshell.
If someone refers to an electron in n=3, l=1, and ml=-1, that electron is in the orbital 3px.
ms is the magnetic spin quantum number. This one specifies the rotation of the electron in an orbital. In one orbital, there are two electrons at max and they must have different spin values. ms=-1/2 refers to an electron spinning down and ms=+1/2 refers to an electron spinning up.
And that's it for quantum numbers. So far, questions we've been asked before with quantum numbers is if a given set of QN values exist or not. For example, if the question gives n=1 and l=2, you know something is off because n=1 cannot have l=2. Some questions will also ask you to name the orbital given a set of quantum numbers, which I've already given an example of when talking about magnetic quantum number.
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