Final answer:
The dyz orbital is one of the five d orbitals and is oriented between the y and z axes. It has a four-leaf clover shape with lobes of opposite phases indicated by different shading. This orbital is initially degenerate with others but may have a different energy in octahedral ligand arrangements.
Step-by-step explanation:
The d-orbitals are regions in space where there is a high probability of finding an electron. In the case of the dyz orbital, it is shaped like a four-leaf clover and is oriented between the y and z axes. This means that the lobes of the dyz orbital lie in the plane that is perpendicular to the x-axis. When drawing the dyz orbital, it is important to include the Cartesian coordinate system with the x, y, and z axes labeled. The orbital will have two lobes along the positive and negative y-axis, and two lobes along the positive and negative z-axis. The phases of these lobes are indicated by different shading or colors, with adjacent lobes having opposite phases.
Remember that all five d orbitals (dx2-y2, dz2, dxy, dxz, and dyz) are initially degenerate, meaning they have the same energy. However, when considering a transition-metal ion in an octahedral arrangement of ligands, the energies of these d orbitals can split into two sets: the eg orbitals (which include the dx2-y2 and dz2 orbitals) and the t2g orbitals (dxy, dxz, and dyz).