Estimated Time to Read: 5 min Atomic Orbitals Three things happen to atomic orbitals as n increases: They become larger, extending farther from the nucleus. They become higher in energy because of their increased distance from the nucleus. They contain more radial nodes. s Orbitals (l=0) s orbitals are spherically symmetrical. They have no angular nodes but may have radial nodes. Orbitals are generally drawn as three-dimensional surfaces that enclose 90% of the electron density, as was shown for the hydrogen 1 s , 2 s , and 3 s orbitals in Figure 1.3.2 b. Although such drawings show the relative sizes of the orbitals, they do not normally show the spherical nodes in the 2 s and 3 s orbitals because the spherical nodes lie inside the 90% surface. p Orbitals (l=1) As the value of l increases, the number of orbitals in a given subshell increases, and the shapes of the orbitals become more complex. p orbitals have a two-lobed shape split by an angular nodal plane. p orbitals may have radial nodes, depending on the value of n . For the 2 p subshell l = 1, so there are three values of m l (−1, 0, and +1), and there are three 2 p orbitals. Figure \(\PageIndex{1}\) depicts a 2 p orbital.Because this orbital has two lobes of electron density arranged along the z axis, with an electron density of zero in the xy plane (i.e., the xy plane is a nodal plane), it is a \(2p_z\) orbital. Figure \(\PageIndex{2}\) shows the contour surfaces, which enclose 90% of the total electron probability, for all three 2 p orbitals. All orbitals have identical shapes just one nodal plane. In each case, the phase of the wave function for each of the 2 p orbitals is positive for the lobe that points along the positive axis and negative for the lobe that points along the negative axis. It is important to emphasize that these signs correspond to the phase of the wave that describes the electron motion, not to positive or negative charges. Each orbital is oriented along the axis indicated by the subscript, and the nodal plane that is perpendicular to that axis bisects each 2 p orbital. The shapes of the 90% probability surfaces of the 3 p , 4 p , and higher-energy p orbitals are essentially the same as those shown in Figure \(\PageIndex{2}\). d Orbitals (l=2) Subshells with l = 2 have five d orbitals; the first principal shell to have a d subshell corresponds to n = 3. The five d orbitals have m l values of −2, −1, 0, +1, and +2. The hydrogen 3d orbitals, shown in Figure \(\PageIndex{3}\), have more complex shapes than the 2p orbitals. All five 3d orbitals contain two nodal surfaces, as compared to one for each p orbital and zero for each s orbital. For three of the d orbitals, the lobes of electron density are oriented between the xy, xz, and yz planes; these orbitals are referred to as the \(3d_{xy}\), \)3d_{xz}\), and \(3d_{yz}\) orbitals, respectively. A fourth d orbital has lobes lying along the x and y axes; this is the \(3d_{x^2−y^2}\) orbital. The fifth 3d orbital, called the \(3d_{z^2}\) orbital, has a unique shape: it looks like a \(2p_z\) orbital combined with an additional doughnut of electron probability lying in the xy plane. Despite its peculiar shape, the \(3d_{z^2}\) orbital is mathematically equivalent to the other four and has the same energy. In contrast to p orbitals, the phase of the wave function for d orbitals is the same for opposite pairs of lobes. For the (dz^2\) orbital, the phase of the wave function is positive for the two lobes that lie along the z axis, and the phase of the wave function is negative for the doughnut of electron density in the xy plane. Like the s and p orbitals, as n increases, the size of the d orbitals increases, but the overall shapes remain similar to those depicted in Figure \(\PageIndex{3}\). f Orbitals (l=3) Principal shells with n = 4 can have subshells with l = 3 and m l values of −3, −2, −1, 0, +1, +2, and +3. These subshells consist of seven f orbitals. Each f orbital has three nodal surfaces, so their shapes are complex. Because f orbitals are not particularly important for our purposes, we do not discuss them further, and orbitals with higher values of l are not discussed at all.