16 ATOMIC ORBITAL THEORY 1.36 d ORBITALS Orbitals having an angular momentum /equal to 2 and,therefore,magnetic quantum numbers,(m of +2.+1,0.-1,-2.These five magnetic quantum numbers describe the five degenerate d orbitals.In the Cartesian coordinate system,these orbitals are desig ated as de d and d:the last four of the d orbitals are characterized by two nodal planes. hil thehas surfaces of revolution. Example.The five d orbitals are depicted in Fig.1.36.The d orbital that by con- vention is the sum of d and d and,hence,really d is strongly directed along the z-axis with a negative"doughnut"in the xy-plane.The dorbital has lobes pointed along thex-and y-axes,while the ddanddorbitals have lobes that are pointed half-way between the axes and in the planes designated by the subscripts 02 d Figure 1.36.The five d orbitals.The shaded and unshaded areas represent lobes of different signs. 1.37 fORBITALS Orbitals having an angular momentum equal to 3 and,therefore,magnetic quantum numbers,m of +3,+2,+1,0,-1,-2,-3.These seven magnetic quantum numbers 1.36 d ORBITALS Orbitals having an angular momentum l equal to 2 and, therefore, magnetic quantum numbers, (ml ) of 2, 1, 0, 1, 2. These five magnetic quantum numbers describe the five degenerate d orbitals. In the Cartesian coordinate system, these orbitals are designated as dz2, dx2  y2, dxy, dxz, and dyz; the last four of these d orbitals are characterized by two nodal planes, while the dz2 has surfaces of revolution. Example. The five d orbitals are depicted in Fig. 1.36. The dz2 orbital that by con￾vention is the sum of dz2  x2 and dz2  y2 and, hence, really d2 z2 x2  y2 is strongly directed along the z-axis with a negative “doughnut” in the xy-plane. The dx2  y 2 orbital has lobes pointed along the x- and y-axes, while the dxy, dxz, and dyz orbitals have lobes that are pointed half-way between the axes and in the planes designated by the subscripts. 1.37 f ORBITALS Orbitals having an angular momentum l equal to 3 and, therefore, magnetic quantum numbers, ml of 3, 2, 1, 0, 1, 2, 3. These seven magnetic quantum numbers 16 ATOMIC ORBITAL THEORY y z x dz2 dx2−y2 dxy dxz dyz Figure 1.36. The five d orbitals. The shaded and unshaded areas represent lobes of different signs. c01.qxd 5/17/2005 5:12 PM Page 16