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building up principle is defined in the following form for, for example, Scandium (21):

[tex]3d^{1}4s^{2}[/tex]

building up principle defines:

[tex]4s < 3d[/tex]

so, the energy of [tex]4s[/tex] level should be smaller than for [tex]3d[/tex]

the energy is defined as:

[tex]e[\text{n$\_$},\text{j$\_$},\alpha \_,\text{z$\_$}]\text{:=}\frac{-13.6*z^2}{n^2}\left(1+\frac{\alpha ^2}{n^2}\left(\frac{n}{j+1/2}-\frac{3}{4}\right)\right)[/tex]

so for n = 4 and l = 0, j = 1/2

for n = 3 and l = 2, j = 3/2, 5/2

e[4, 1/2, 1/137, 21] = -374.854

e[3, 3/2, 1/137, 21] = -666.403

help me to find mistake, thank you!

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# Building Up Principle & Fine Splitting

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