energy of the three orbitals are identical. They differ however, in the way the lobes are oriented. Since the lobes may be considered to lie along the x, y or z axis, they are given the designations p x , p y , and p z . It should be understood, however, that there is no simple relation between the values of m l (– , and + ) and the x, y and z directions.
For our purpose, it is sufficient to remember that, because there are three possible values of m l , there are, therefore, three p orbitals whose axes are mutually perpendicular. Like s orbitals, p orbitals increase in size and energy with increase in the principal quantum number and hence the order of the energy and size of various p orbitals is p > p > p . Further, like s orbitals, the probability density functions for p -orbital also pass through value zero, besides at zero and infinite distance, as the distance from the nucleus increases. The number of nodes are given by the n – , that is number of radial node is for p orbital, two for p orbital and so on.
For l = , the orbital is known as d -orbital and the minimum value of principal quantum number ( n ) has to be . as the value of l cannot be greater than n – . There are five m l values (– , – , , + and + ) for l = and thus there are five d orbitals. The boundary surface diagram of d orbitals are shown in Fig.
. . The five d -orbitals are designated as d xy , d yz , d xz , d x2–y2 and d z2 . The shapes of the first four d -orbitals are similar to each other, where as that of the fifth one, d z2 , is different from others, but all five d orbitals are equivalent in energy.
The d orbitals for which n is greater than ( d