The quantum that divides shells into orbitals is the "Azimuthal" quantum number, also known as the "angular momentum" quantum number.
The azimuthal quantum number determines the shape of an electron's orbital, which is a region in space where there is a high probability of finding an electron. It describes the angular momentum of an electron in an atom and the number of subshells within a given shell. Each subshell is associated with a specific shape, and can hold a certain number of electrons.
The azimuthal quantum number is represented by the letter "l" and can have integer values ranging from 0 to (n-1), where "n" is the principal quantum number. Each value of "l" corresponds to a different subshell shape:
- l = 0 corresponds to an "s" subshell, which is spherical in shape.
- l = 1 corresponds to a "p" subshell, which has a dumbbell shape with two lobes.
- l = 2 corresponds to a "d" subshell, which has a more complex shape with four lobes and a doughnut-like ring.
- l = 3 corresponds to an "f" subshell, which has an even more complex shape with eight lobes.
The number of orbitals within a subshell is equal to 2l+1. For example, a "p" subshell (l = 1) has three orbitals (2l+1 = 3), which are labeled as "px", "py", and "pz".
In summary, the azimuthal quantum number determines the shape of the electron's orbital and the number of subshells within a given shell, and it is represented by the letter "l".