# Building Up Principle & Fine Splitting

1. Apr 3, 2010

### LMZ

Hi 2 all,

building up principle is defined in the following form for, for example, Scandium (21):
$$3d^{1}4s^{2}$$

building up principle defines:
$$4s < 3d$$

so, the energy of $$4s$$ level should be smaller than for $$3d$$

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

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!