Filling of Electronic States - usual filling sequence: - consider ...
Filling of Electronic States - usual filling sequence: - consider ... Filling of Electronic States - usual filling sequence: - consider ...
Hyperfine structure - atomic nuclei also have intrinsic angular moments and magnetic moments - these also contribute to the total angular moments - the angular moments are small and thus make only small (but observable and also useful) contributions to the total energy of electrons - the three sources of angular momentum in an atom phys4.10 Page 11 Term Symbols - as for single electron states symbols are used to indicate the total orbital angular momentum of a many electron atom - in this case capitalized letters are used - a superscript number before the letter indicates the multiplicity of the state, i.e. the number of possibilities to combine the total L and total S to a total angular momentum J - for L > S the total momentum ranges from L - S to L + S, i.e. the multiplicity is 2 S + 1 - in the situation S = 0 the multiplicity is 1, hence there is only one state with J = L that is called a singlet - for S = 1/2 there is a doublet state (L+ 1/2, L - 1/2) - for S = 1 there is a triplet state (L+ 1, L, L - 1) phys4.10 Page 12
- for S > L the multiplicity is given by 2 L + 1 - the total angular momentum of the state realized is then indicated by a subscript after the letter - example: 'doublet P three halves' - in atoms with a single outer shell electron the principal quantum number is used as a prefix - e.g. in sodium (Na) phys4.10 Page 13 Find the different possible values of J for two electrons in with orbital quantum numbers l 1 = 1 and l 2 = 2 and spin quantum numbers s 1,2 = ± 1/2. - three different possibilities to form L = |l 1 - l 2 | … |l 1 + l 2 | = 1, 2, 3 - two possibilities to form S = |s 1 - s 2 | … |s 1 + s 2 | = 0, 1 - orbital and spin angular moments - five possibilities to form J = |L - S| … |L + S| = 0, 1, 2, 3, 4 phys4.10 Page 14
- Page 1 and 2: Filling of Electronic States - usua
- Page 3 and 4: Spin orbit coupling in hydrogen - n
- Page 5: LS coupling - in many electron atom
- Page 9 and 10: Helium (He, Z = 2 ) spectrum: selec
Hyperfine structure<br />
- atomic nuclei also have intrinsic angular moments and magnetic moments<br />
- these also contribute to the total angular moments<br />
- the angular moments are small and thus make only small (but observable and also useful)<br />
contributions to the total energy <strong>of</strong> electrons<br />
- the three sources <strong>of</strong> angular momentum in an atom<br />
phys4.10 Page 11<br />
Term Symbols<br />
- as for single electron states symbols are used to indicate the total orbital angular<br />
momentum <strong>of</strong> a many electron atom<br />
- in this case capitalized letters are used<br />
- a superscript number before the letter indicates the multiplicity <strong>of</strong> the state, i.e. the number<br />
<strong>of</strong> possibilities to combine the total L and total S to a total angular momentum J<br />
- for L > S the total momentum ranges from L - S to L + S, i.e. the multiplicity is 2 S + 1<br />
- in the situation S = 0 the multiplicity is 1, hence there is only one state with J = L that is<br />
called a singlet<br />
- for S = 1/2 there is a doublet state (L+ 1/2, L - 1/2)<br />
- for S = 1 there is a triplet state (L+ 1, L, L - 1)<br />
phys4.10 Page 12
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