8. The Machinery Behind The      Periodic Table   Previous PageNext Page
     The Better Theory: Wave Mechanics

The five orbitals for I = 2, or d orbitals, are more complicated. If we define a set of perpendicular x, y, and z coordinates, then the , , and orbitals, have cloverleaf electron probability distributions in the xy, yz, and xz planes respectively, as shown opposite. The orbital has highest probability along the x and y axes, and the has maximum electron probability along the z axis. The f and higher orbitals are even more complicated, but never need to be visualized in any practical chemical situation. The s, p, and d orbital shapes are sufficient for our purposes, and you should know these well.

The illustrations shown on this page represent electron probabilities, or values of the square of the wave function, . These values always are positive, whereas the original wave function, , can be positive or negative. The signs of in various lobes of the probability functions are indicated by + and - signs. Whether the sign is positive or negative is not significant, but the change in sign from one lobe of probability to the next is. The signs of the wave functions become necessary as soon as we begin to combine atoms to form molecules, as in the next chapter.

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