we have 4 quantum numbers as mentioned before.
n L m s

n is a given quantized energy level
L = (n-1)
-L < m < L greater than or equal (no character for it)
s = +1/2 , -1/2 (2 electrons for each m)

when n=1 as for H or He
L = 0
m = 0
s = +1/2, -1/2

so for the n=1 level only 2 electrons possible hence just 1s

for n=2
L = 1
m = -1,0,1
s = +1/2, -1/2

so for n=2 level we can have 6 electrons
m=-1 +1/2, -1/2 spins = 2 electrons
m=0 +1/2, -1/2 spins = 2 electrons
m=1 +1/2, -1/2 spins = 2 electrons

for n=3
L=2
m=-2,-1,0,1,2
s = +1/2, -1/2

m=-2 +1/2, -1/2 spins = 2 electrons
m=-1 +1/2, -1/2 spins = 2 electrons
m=0 +1/2, -1/2 spins = 2 electrons
m=1 +1/2, -1/2 spins = 2 electrons
m=2 +1/2, -1/2 spins = 2 electrons

you get 10 total electrons forming the d-orbitals at n=3

for n=4
L=3
m=-3,-2,-1,0,1,2,3
s = +1/2, -1/2

so 14 total electrons hence forming the f-orbitals at the n=4 level

For an atom, you must consider ALL the numbers. Those cases above were only for the outer most electron shell. In other words, your atom even if the ground state valence shell electrons are n=4, you must consider n=3,2,1 as those electrons are still present.

In basic form as proved above
L=0 for s shells
L=1 for p shells
L=2 for d shells
L=3 for f shells

P.S. You plug in the n,L,m,s numbers into Schroedinger's Wave equations which in turn will do nothing but give you a big headache. Heck, for Hydrogen, its a full page of 20 seperate equations or so. Its those silly physcist complicating things.

Thanks Scarf. I truly understand what you mean. But how if n=0?

n = 0 doesn't mean anything!

we starting counting from 1 ....... before that, there isn't anything there! -)

Between matter and antimatter, there's something inside, namely period 0 with an 'element-loid' Neutron. It exists as 2 isotopes: A1Z0 (single free) neutron and A4Z0 Tetraneutron (4 neutrons staying together as the shape of Helium nuclei).

Therefore I think 0 does mean something.

Your getting ahead of yourself. Your dwelling into the realm of the sub-atomic physicist.

when n=0 there are no electronic states. Schroeding's equations / quantum mechanics fails us, as they apply only to electron / electrons. They are no longer valid.

Its always fun to dive into questions like that, but I've realized they are only applicable to theorectial physicist models that have no real world applications or uses (I'm a very conceptual thinking person).

Also, I'm a very poor speller, so I'm sorry if you haven't been able to find some words in your translation dictionary.

Much thanks then. I thought quantum numbers work not only in electrons before you told me they don't.

It is pleasant for me very much, how feline 1 explains a structure of electronic shells, but as it seems to me, all this is far from a reality.
This is very appreciable distinction, how physicists and chemists understand the word orbital.
At reading of textbooks and articles by many authors-chemists each reader can find out, that chemists involuntarily (subconsciously) put the equal-sign between the words orbital and orbit of curvilinear movement.
I would like to bring for your attention some pictures, which "were drawn" with the mathematical program "MATHCAD".
During the whole year I occasionally look through these pictures and cannot understand, what benefit can be taken from these orbits and orbitals:
http://vlamir.nsk.ru/pt4_film.gif (80.5Kb)
It is the closed resonant object, which has constant length. The amplitude of oscillations cannot be more than some limit n, which in scale is shown in figure
http://vlamir.nsk.ru/pt4xn.gif (6.5Kb)
These two figures precisely correspond to experiment.
Attempts to increase amplitude of oscillations are ineffectual since for this purpose it is necessary to break off the orbit.
But the mathematical program makes it very simply.
In the following three figures the amplitude of oscillations is increased in six, twelve and twenty times, accordingly:
http://vlamir.nsk.ru/pt4x6.gif (7.5Kb)
http://vlamir.nsk.ru/pt4x12.gif (7.0Kb)
http://vlamir.nsk.ru/pt4x20.gif (6.5Kb)
With the help of the polytronic equations we can create huge set of similar projections with various number of petals, which, as you see, are similar standard orbitals. My doubts in a reality and stability of these energy states of atoms are based that for creation of these conditions the atoms or their some parts (for example, electronic orbits and shells) should be destroyed.
On the other hand, I should trust mathematics.

Trust it but not totally. It was said that there were only rational numbers, then rational numbers and irrational numbers fill the number line together, now there are some numbers which are not on the number line at all.

If we shall digress from the electronic paradigm, then we can sort and rearrange elements on other allied physical and chemical properties.
In this case we shall receive absolutely other numerical lines.
For example:
H

Irrational (complex) numbers occur in the Schroedinger wave equations for numerous orbitals...