Question

Eletron density of d orbitals

Answer 1

The first set of d orbitals is the 3d set. The angular momentum quantum number is 2, so each orbital has two angular nodes. There are 5 choices for the magnetic quantum number, which gives rise to 5 different d orbitals. Each orbital can hold two electrons (with opposite spins), giving the d orbitals a total capacity of 10 electrons.

{\displaystyle {\begin{matrix}n&=&3,4,5,...\\l&=&2\\m_{l}&=&-2,-1,0,1,2\\m_{s}&=&+{\frac {1}{2}},-{\frac {1}{2}}\\\end{matrix}}} {\displaystyle {\begin{matrix}n&=&3,4,5,...\\l&=&2\\m_{l}&=&-2,-1,0,1,2\\m_{s}&=&+{\frac {1}{2}},-{\frac {1}{2}}\\\end{matrix}}}

Note that all the d orbitals have four lobes of electron density, except for the dz2 orbital, which has two opposing lobes and a doughnut of electron density around the middle. The d orbitals can be further subdivided into two smaller sets. The dx2-y2 and dz2 all point directly along the x, y, and z axes. They form an eg set. On the other hand, the lobes of the dxy, dxz and dyz all line up in the quadrants, with no electron density on the axes. These three orbitals form the t2g set. In most cases, the d orbitals are degenerate, but sometimes they can split, with the eg and t2g subsets having different energy. Crystal Field Theory predicts and accounts for this. D orbitals are sometimes involved in bonding, especially in inorganic chemistry.