p31318notes11.pdf - 9 Addition of a p electron(l = 1...

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9 Addition of a p electron ( l = 1, magnitude = 2 ) to a d electron ( l = 1, magnitude = 6 ) The quantum number L associated with the resultant vector L must be integral and of magnitude ) 1 ( + L L . The largest value of L is 3 2 1 = + l l , and the smallest is . 1 2 1 = - l l All integral values between these limits (there is only one such value, namely 2) are possible. 3 , 2 , 1 1 2 2 1 = = = L l l
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8 2 3 2 1 2 = s L = 2 6 d l 1 = 2 6 d l 1 = 2 6 p l 2 = 1 2 p l 2 = 1 2 L = 1 2 p l 2 = 1 2 L = 3 12 2 3 2 1 1 = s S = 1 2 d l 1 = 2 6
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7 If we look at the transition at 587.67 nm (that is the yellow line (sometimes labelled “D 3 - although not by Fraunhofer - observed in the flash spectrum of the chromosphere), we see that it is a transition between two terms of three levels each. Thus we may suppose that it is not actually a single line, but several lines close together. Perhaps it is actually nine lines? In fact, there are fewer than nine lines, because some of the transitions are forbidden by selection rules. No need for more details here, since it is difficult to resolve these lines in this particular case. In heavier atoms the several lines connecting two terms are more easily separated, and we shall be discussing such cases later. In the meantime, some words and some notation. A term is defined by LS , such as 3 D. A term consists of 1 ) , min( 2 + S L levels each defined by LSJ , such as 3 D 2 . A line is a transition between two levels . The totality of transitions connecting two terms is a multiplet . A line is written thus (for example): 3 P 1 - 3 D 2 . In atomic spectroscopy (but not molecular spectroscopy) the lower level is always written first., whether the line is an emission line or an absorption line. If you want to indicate the direction of a transition, you can use an arrow rather than a dash. A multiplet is written 3 P - 3 D.
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6 1 S 1 1 D 3 S 3 3 D 1083.0 nm 587.67 nm 706.53 nm 667.86 nm 728.12 nm 501.61 nm 1 s 2 s 1 s 3 s 1 s 4 s 1 s 5 s 1 s 5 p 1 s 4 p 1 s 3 p 1 s 2 p 1 s 5 d 1 s 4 d 1 s 3 d 1 s 5 s 1 s 4 s 1 s 3 s 1 s 2 s 1 s 5 p 1 s 4 p 1 s 3 p 1 s 2 p 1 s 2 Orthohelium Parahelium
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