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So my teacher told me that EACH shell contains 5 subshells (s, p, d, f, g) but what I don't understand is this

enter image description here

The 1st shell has only 1 subshell (and not 5 like he said) and the number of subshells keeps increasing as shell levels increase and then number of subshells decreases after 5th shell.

So why did my teacher tell me that EVERY SHELL has 5 subshells when it's not true (according to this and many examples)?

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    $\begingroup$ Your interpretation of the diagram is essentially correct. I can't comment on what your teacher might have said or whether there was miscommunication. $\endgroup$
    – paisanco
    Sep 14, 2014 at 13:51
  • $\begingroup$ So "each shell has 5 subshells" is a lie?It seems that i have bad professors.Anyway why are some subshells faded (5th shell subshell g and below)? $\endgroup$ Sep 14, 2014 at 14:11
  • $\begingroup$ None of the elements discovered so far, has any electrons in the g subshell in the ground state. $\endgroup$
    – LDC3
    Sep 14, 2014 at 14:17
  • $\begingroup$ The number of sub-shells doesn't decrease after the fifth shell --- the lines that are greyed out should be continued downwards until they are left-aligned with all the others --- this is perhaps the reason that they are greyed out. The number of sub-shells per shell is $n^2$, where $n$ is the principal quantum number of the shell. Your teacher may have made a mistake, or perhaps you misunderstood them. $\endgroup$
    – gj255
    Sep 17, 2014 at 10:31

1 Answer 1

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In quantum mechanics, one can form a solid understanding of these matters. The conceptually simplest example which demonstrates the essential physics is, of course, the hydrogen atom. In solving it, we find that the (spatial part of the) allowed eigenstates of the Hamiltonian are parametrized by three quantum numbers, $n$, $\ell$ and $m$. So, we have $\psi_{nlm}$ In the mathematical derivation, one is forced to assume the following things:

  1. $n \in \mathbb{Z_+}$
  2. $\ell=0,1,\dots,n-1$
  3. $m=-\ell,-\ell+1,\dots,\ell-1,\ell$

Now, each different value of $n$ corresponds to an electron shell. As we can see, $n=1$ allows only $\ell=m=0$. Some people (e.g. chemists, but also many physicists) like to replace the labels $\ell=0,1,2,3,4,\dots$ with the labels $s,p,d,f,g,\dots$, but there is really no conceptual difference here.

Now, the Pauli exclusion principle tells us that electrons cannot occupy the exact same state. So, one is led to the conclusion that the lowest energy shell allows only a single electron. Due to spin (each electron can have spin $\uparrow$ or $\downarrow$) there are actually two allowed electrons in the lowest shell, but this is not an essential point here. What should be clear is that the number of allowed $\ell$-values depends on $n$, and is certainly not always five.

The way the allowed electron states are actually 'filled up' in practical situations involving atoms more complex than hydrogen, are of course generally hard to understand (analytically), and the states are often not filled up in the order one might expect from the labeling system (i.e. first filling all $n=4$ before any $n=5$ states), but these issues are not essential here.

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  • $\begingroup$ +1 but the OP stated they were a high school student so there may be a need to clarify some terms. $\endgroup$
    – paisanco
    Sep 14, 2014 at 14:20
  • $\begingroup$ @paisanco this is why I did not include the actual derivation of the quantum numbers ;) $\endgroup$
    – Danu
    Sep 14, 2014 at 14:21
  • $\begingroup$ It's just the use of notation like $\in$ and $\mathbb{Z}_+$ that is perhaps unnecessary and confusing. $\endgroup$
    – gj255
    Sep 17, 2014 at 10:32

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