Building Up Principle & Fine Splitting

[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!

 

[eljose79]

Hello,

I can help you understand the building up principle and the energy levels for Scandium (Sc). The building up principle is a concept in chemistry that explains the arrangement of electrons in an atom's orbitals. It states that electrons will fill the lowest energy orbitals first before moving to higher energy orbitals.

In the case of Scandium, it has 21 electrons. According to the periodic table, Scandium's electron configuration is 1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^1. This means that the first 2 electrons will fill the 1s orbital, the next 2 will fill the 2s orbital, the next 6 will fill the 2p orbital, and so on.

The energy levels for each orbital are determined by the equation you provided. However, there is a mistake in the values you used for n, l, and j. For the 4s orbital, n = 4, l = 0, and j = 1/2. For the 3d orbital, n = 3, l = 2, and j = 3/2 or 5/2. When you plug in these values, you should get e[4, 1/2, 1/137, 21] = -374.854 and e[3, 5/2, 1/137, 21] = -666.403.

I hope this helps clarify the building up principle and the energy levels for Scandium. Let me know if you have any further questions. Happy researching!