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A350597 Irregular triangle read by rows in which row n lists the partial sums of shell numbers and respective number of electrons for all occupied shells of the n-th element of the periodic table of the elements where electron configurations are ordered according to Madelung's rule.

%I A350597 #19 Nov 28 2024 10:56:09
%S A350597 1,2,1,3,1,3,5,6,1,3,5,7,1,3,5,7,9,10,1,3,5,7,9,11,1,3,5,7,9,12,1,3,5,
%T A350597 7,9,13,1,3,5,7,9,14,1,3,5,7,9,15,1,3,5,7,9,15,18,19,1,3,5,7,9,15,18,
%U A350597 20,1,3,5,7,9,15,18,20,23,24,1,3,5,7,9,15,18,20,23,25
%N A350597 Irregular triangle read by rows in which row n lists the partial sums of shell numbers and respective number of electrons for all occupied shells of the n-th element of the periodic table of the elements where electron configurations are ordered according to Madelung's rule.
%C A350597 This sequence is a variant of A335105.
%C A350597 This sequence agrees with A335105 until the row for scandium; specifically, divergence occurs at t(20,10).
%C A350597 Electron configurations are either written in spectroscopic order as in A335105 where configurations are listed in order of increasing values of the main quantum number, or by order of Madelung's rule, where they are written in order of increasing values of the sums of the main quantum number and respective angular momentum numbers (s,p,d or f) with s=0, p=1, d=2, f=3. Thus in Madelung order 4s (sum 4+0) is written ahead of 3d (sum 3+2).
%C A350597 The final term of each row of this sequence agrees with final term of each row of A335105.
%D A350597 Gary L. Miessler and Donald A. Tarr, Inorganic Chemistry, 4th Edition. Prentice Hall. Upper Saddle River, New Jersey, 2011.
%D A350597 John R. Rumble (ed.), CRC Handbook of Chemistry and Physics, 100th edition. CRC Press. Boca Raton, Florida, 2019; Section 1, Electron Configurations and Ionization Energy of Neutral Atoms in the Ground State.
%D A350597 Eric Scerri, The Periodic Table, 2nd edition. Oxford University Press. New York, New York, 2019.
%e A350597 The configuration for lithium is 1s2 2s1 whether written in spectroscopic order or by order of the Madelung rule. Thus the row for lithium in A335105 and the row for lithium in this sequence agree being derived as follows:
%e A350597   1s2 2s1
%e A350597   1+2+2+1
%e A350597   1, 3, 5, 6
%e A350597   However: in spectroscopic order scandium is written 1s2, 2s2, 2p6, 3s2, 3p6, 3d1, 4s2 yielding a row in A335105 of 1, 3, 5, 7, 9, 15, 18, 20, 23, 29, 32, 33, 37, 39, whereas in Madelung order the same algorithm applied to the configuration for scandium yields a row of 1, 3, 5, 7, 9, 15, 18, 20, 23, 29, 33, 35, 38, 39.
%Y A350597 Cf. A335105.
%K A350597 nonn,tabf
%O A350597 1,2
%A A350597 _David Williams_, Jan 08 2022