Orbital Wave Functions and Shapes of Orbitals


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According to wave mechanics, orbitals are described by wave functions known as orbital wave functions. These orbital wave functions can be represented as a product of two functions: (i) Radial wave function and (ii) Angular wave function.

The radial wave function depends upon the distance (r) from the nucleus whereas angular wave function depends upon the direction given by angles with respect to different axes. The complete wave function represents an orbital in which radial part gives the size and the angular part gives its shape. It is observed that the wave function for s-orbital is independent of angles and therefore, s-orbitals do not have angular dependence. Thus, all s orbitals are spherically symmetrical. However, all other types of orbitals (p or d) have angular dependence and, therefore, have directional dependence.



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