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

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)? 
 A: 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:


*

*$n \in \mathbb{Z_+}$

*$\ell=0,1,\dots,n-1$

*$m=-\ell,-\ell+1,\dots,\ell-1,\ell$


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.
