[talanum1 (OP)]

The picture at "Atoms and Molecules" at: https://en.wikipedia.org/wiki/Electro, is wrong: the third row and the fifth row should be excluded because the table of the element's numbers go like:

2, 2, 6, 2, 6, 2, 10, 6, ...

and the f-level's row has 14 blocks.

This means the formulae is also not right: only a subset of the formulae get used.

Also to get the wave function of the second 6 and third 2 for example, we would need a sum of the given orbital wave functions.

[hamdani yusuf]

The link only refers to a disambiguation page. Can you just insert the picture here?
You can use insert image icon after you press the preview button.

[talanum1 (OP)]

The picture is attached in .png  format.

[Bored chemist]

You refer to a table...

[talanum1 (OP)]

You refer to a table...

Yes, the Periodic Table of the Elements: this reflects electron orbitals in an atom.

[talanum1 (OP)]

I may be wrong: I considered them in the sequence they appeared in.

[talanum1 (OP)]

Anyway there is an error in the formula: r should be roh.

[chiralSPO]

Using quantumn numbers n, l, m_l and m_s, we would expect:
2
2, 6
2, 6, 10
2, 6, 10, 14
2, 6, 10, 14, 18
etc.

But, because both n and l contribute to the energy of the electrons, it turns out that when placed in order of energy, it becomes:
2
2, 6
2, 6
2, 10, 6
2, 10, 6
2, 14, 10, 6
2, 14, 10, 6
2, 18, 14, 10, 6

[talanum1 (OP)]

But, because both n and l contribute to the energy of the electrons, it turns out that when placed in order of energy, it becomes:22, 62, 62, 10, 62, 10, 62, 14, 10, 62, 14, 10, 62, 18, 14, 10, 6

That is the order of the Periodic Table of the Elements. To be picky: mathematically there should be another row of "2" at the top.

[talanum1 (OP)]

Are the numbers in the picture in order: (n, l, m_l)?

[talanum1 (OP)]

(3, 0, 0), (2, 1, 0) and (2, 1, 1) should be grouped together as the 2p orbitals. I was wrong, the pictures are just not in the order of the Periodic Table of the Elements.

[Bored chemist]

Anyway there is an error in the formula: r should be roh.

Do you mean rho (ρ) ?

[talanum1 (OP)]

Yes I meant rho (ρ).

No to my previous post, the 2p orbitals all have n = 3. In which case (2, 1, 0) and (2, 1, 1) must be superpositions of 2s and 2p or wrong?