Mathematical expressions for angular wave functions for d-orbital’s are complex and have been left out*. For= 2, m has five values 0, 1, 2 representing the five orientations of d-orbital’s designated as . Their angular dependence is more complicated than that of p-orbital. Probability surface diagrams of three orbital’s d_xy , d_yz and d_xz have four lobes of high electron density in xy, yz and ax planes, respectively with each lobe bisecting the principal axes into two equal hal ves.

The fourth d-orbital  has four lobes of electron density is xy plane along the x and y-axes. The fifth d-orbital d_x² has a different shape. It has two lobes along the z-axis with a ring of electron density around the nucleus in xy plane. It may be pointed out for your information that d_z² can be taken as a linear combination of two orbitals d_y²-z² and d_z²-x² each of which ahs our lobes with orientation of d_x²-y² along the distribution of electron density. Each of the d-orbitals possesses two nodal planes.

                                                            Shapes of d-orbitals

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