The angular momentum quantum number l

The angular momentum quantum number l describes the shape of the orbital, and the shape is limited by the principal quantum number n: The angular momentum quantum number l can have positive integer values from 0 to n – 1.

  For example, if the n value is 3, three values are allowed for l: 0, 1, and 2. The value of l defines the shape of the orbital, and the value of n defines the size.  Orbitals that have the same value of n but different values of l are called subshells. These subshells are given different letters to help chemists distinguish them from each other. Table 1.1 shows the letters corresponding to the different values of l.

Table 1-1 Letter Designation of the Subshells

  When chemists describe one particular subshell in an atom, they can use both the n value and the subshell letter — 2p, 3d, and so on. Normally, a subshell value of 4 is the largest needed to describe a particular subshell. If chemists ever need a larger value, they can create subshell numbers and letters. Figure 1.1 shows the shapes of the s, p, and d orbitals. In Figure 1.1a, there are two s orbitals — one for energy level 1 (1s) and the other for energy level 2 (2s). S orbitals are spherical with the nucleus at the center. Notice that the 2s orbital is larger in diameter than the 1s orbital. In large atoms, the 1s orbital is nestled inside the 2s, just like the 2p is nestled inside the 3p.

Figure 1.1b shows the shapes of the p orbitals, and Figure 1.1c shows the shapes of the d orbitals. Notice that the shapes get progressively more complex.

Figure 1.1: Shapes of the s, p, and d orbitals.