Electron shell
In atomic spectroscopy, an electronic shell is set of spatial orbitals with the same principal quantum number n. There are n2 spatial orbitals in a shell, see hydrogen-like atoms. For instance, the n = 3 shell contains nine orbitals: one 3s-, three 3p-, and five 3d-orbitals. A shell is closed if all orbitals in it are doubly occupied, once with spin up (α) and once with spin down (β). For example, the closed n = 1, 2, and 3 shells contain 2, 8, and 18 electrons, respectively.
An atomic subshell is a set of 2l+1 spatial orbitals with a given principal quantum number n and a given orbital angular momentum quantum number l. A subshell is closed, if there are 2(2l+1) electrons in the subshell.For instance the 2p subshell in the neon atom contains 6 electrons and hence it is closed. Likewise in the cupper atom the 3d subshell is closed (contains 10 electrons). A subshell l with number of electrons N, with 1 ≤ N < 2(2l+1), is called open. The fluorine 2p subshell, with electronic configuration 2p5, is open.
A closed subshell is an eigenstate of total orbital angular momentum operator squared L2 with quantum number L = 0. That is, the eigenvalue of L2, which has the general form L(L+1), is zero. A closed subshell is also an eigenstate of total spin angular momentum operator squared S2 with quantum number S = 0. That is, the eigenvalue of S2, which has the general form S(S+1), is zero. The proof of these two statements will be omitted. Briefly, they rest on the fact that closed (sub)shells have wavefunctions that are Slater determinants which are invariant under the action of L and S.