Concept of Shells and Subshells

In the fuller quantum mechanical picture, Bohr's orbits are reinterpreted as shells, and each shell is further divided into one or more subshells.

Shells. A shell is the set of all orbitals that share the same value of the principal quantum number $n = 1, 2, 3, \ldots$. Shells are also traditionally labelled by letters, $K, L, M, N, \ldots$ for $n = 1, 2, 3, 4, \ldots$ respectively. The principal quantum number chiefly determines the size of the shell (how far, on average, its electrons lie from the nucleus) and, for a given atom, its energy: the larger $n$ is, the larger and (in a one-electron atom) the higher in energy the shell is. A shell with principal quantum number $n$ can hold a maximum of $2n^2$ electrons.

Subshells. Each shell is itself split into subshells, labelled by the azimuthal (or orbital angular momentum) quantum number $l$, which can take any integer value from $0$ to $(n-1)$ for a given $n$. Subshells are referred to by letters rather than numbers: $l = 0$ is called the $s$ subshell, $l = 1$ the $p$ subshell, $l = 2$ the $d$ subshell, and $l = 3$ the $f$ subshell. So, for example, the $n = 3$ (M) shell has three subshells: $3s$ ($l=0$), $3p$ ($l=1$) and $3d$ ($l=2$); the $n = 4$ (N) shell has four: $4s, 4p, 4d, 4f$. In general, the shell with principal quantum number $n$ has exactly $n$ subshells. …