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“This video we ll discuss atomic term symbols so we discuss term symbols briefly in in our chapter on the hydrogen atom. But now we re back to do it all atoms for arbitrary values of spin orbital angular momentum and total angular momentum. So we have s. Which represents.
Our spinning your momentum capital s. For our entire atom capital l. Represents. The orbital angular momentum of our entire.
Atom and capital. J. Represents. The total angular momentum.
Which is a combination of our spin and orbital parts. So for each of these the value of l. Is greater than or equal to zero. And is an integer s and j are greater than zero and our integers or half integers.
So they either are integers or or some integer. Multiple of one half to get the value of j. For a given value of l. And s.
We do that j is every integer or half integer between l plus s and the absolute value of l minus s each of these then have their component along the z axis m sub s m sub l and m sub j where again if s is a half integer m sub s is all half integers from s 2 minus s l m sub l. Is all integers from l 2 minus l and m sub j. Is all half integers from j 2 minus j. So for atomic values of these things we re going to use capital letters.
So s. For example can take on values of 0 1. 2. Etc.
Or it could take on values of 1 2. 3. Halves. 5.
Halves etc l. Can take on values of 0 1..
2 etc. Which correspond to s. P. D.
F. G. Etc. J.
Can take on values of 0 1. 2. Going up or it could take on values like 1 2. 3.
Halves. 5. Halves. So this is what i mean when i say half integers.
And that it could be multiples of 1. As well alright so combining our values of s l. And j. For a given electronic state of an atom.
We get what we call a term symbol. Term symbols are used to represent distinct electronic states of atoms. So our term symbol is represented in the left by a superscript of two times s. Plus.
1. Then there s a capital letter rip of the letter representing l. Spd. Etc.
Then a on the right a subscript with for capital j. Which is the value of j. That we have for that state. So this 2 s.
Plus 1. Up at the top left..
That s called the multiplicity of the state. If s. Equals. 0.
To s plus. 1. Is 1. That s a singlet to s.
If s. Equals. 1 2. To s plus.
1 is 2. That s a doublet so 1s equals 1 2. Means you can have spin up or spin down two states. If s.
Equals. 1 to s plus. 1. Is.
3. That s a triplet four is a quartet five is a quintet six is a sextet and the trend continues beyond. There. So.
If we have a value where of s. Equals zero. Our multiplicity is 1. We have a singlet and for any given value of l.
Then we re only going to have one value of j. Because the number of the number of j values is determined by the magnitude of s. So we can have things like singlet s0 singlet p1. Singlet d.
To singlet f3. A singlet can only have one term for a given value of thoth of orbital angular momentum for doublets..
We only have doublet s 1 2. For s. But for p. Where l.
Equals. 1. J. Could be three.
Halves or 1 2. 1. Plus. 1.
2. Or. 1 minus. 1.
2. So we get up doublet p. 3. Halves double p 1 2.
Doublet. D5. Halves. Double d.
3 halves. For triplets we get 3 values for each value. 3. Possible values for each angular momentum.
Triplet p. 2. Triplet p. 1.
Triplet p. 0..
Triplet t. 3. Triplet d. 2.
With d1 etc. So for the example of a carbon atom in its ground state. We have 1s2 2s2 2p2 is our ground state electron configuration so the 1s and 2 s sub shells are completely filled. But for the purposes of determining our term symbols.
We re only going to look at partially filled sub shells. So in the next video will show how we show that for a carbon atom. Which has a valence of 2p. It has the possible term symbols.
Singlet. D. Triplet. P.
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