4 quantum numbers: n, l, ml, msPrincipal Quantum Number
The first quantum number is commonly known as the principal quantum number and is denoted by
the letter n. It is used in Bohr’s model and can theoretically take on any positive integer value. The
larger the integer value of n, the higher the energy level and the farther away, on average, you will
find the electron from the nucleus. The maximum number of electrons in energy level n (electron
shell n) is 2n^2.
BASIC CONCEPTS
l = 0: s subshell
l = 1: p subshell
l = 2: d subshell
l = 3: f subshellAzimuthal Quantum Number
The second quantum number is called the azimuthal quantum number and is designated by the
letter l. (It is also known as the angular momentum quantum number.) This quantum number refers
to the subshells or sublevels that occur within each principal energy level. For any given n, the value
of l can be any integer in the range of 0 to (n – 1). For example, the shell of n = 3 can have subshells
with l = 0, l = 1, and l = 2, whereas the shell of n = 1 can only have the subshell l = 0. The four subshells
corresponding to l = 0, 1, 2, and 3 are known as the s, p, d, and f subshells, respectively. Based on the
restriction on l values just discussed, we can see that every shell has an s subshell, while only shells
with n > 1 have p subshells, et cetera. For atoms with more than one electron, the greater the value
of l, the greater the energy of the subshell. However, the energies of subshells from different
principal energy levels may overlap. For example, the 4s subshell may have a lower energy than the
3 d subshell.