, d ...) also have shapes similar to d orbital, but differ in energy and size. Besides the radial nodes (i.e., probability density function is zero), the probability density functions for the n p and n d orbitals are zero at the plane (s), passing through the nucleus (origin). For example, in case of p z orbital, xy-plane is a nodal plane, in case of d xy orbital, there are two nodal planes passing through the origin and bisecting the xy plane containing z-axis. These are called angular nodes and number of angular nodes are given by ‘ l ’, i.e., one angular node for p orbitals, two angular nodes for ‘ d ’ orbitals and so on.
The total number of nodes are given by ( n – ), i.e., sum of l angular nodes and ( n – l – ) radial nodes. . . Energies of Orbitals The energy of an electron in a hydrogen atom is determined solely by the principal quantum Fig.
. Boundary surface diagrams of the five 3d orbitals. number. Thus the energy of the orbitals in hydrogen atom increases as follows : s < s = p < s = p = d < s = p = d = f < ( .
) and is depicted in Fig. . . Although the shapes of s and p orbitals are different, an electron has the same energy when it is in the s orbital as when it is present in p orbital.
The orbitals having the same energy are called degenerate. The s orbital in a hydrogen atom, as said earlier, corresponds to the most stable condition and is called the ground state and an electron residing in this orbital is most strongly held by the nucleus. An electron in the s , p or higher orbitals in a hydrogen atom is in excited state. The energy of an electron in a multi- electron atom, unlike that of the hydrogen atom, depends not only on its principal