and m l = – , – , , + +, + ). Therefore, the total number of orbitals is + + = The same value can also be obtained by using the relation; number of orbitals = n , i.e. = . Problem .
Using s , p , d , f notations, describe the orbital with the following quantum numbers (a) n = , l = , (b) n = , l = , (c) n = , l = , (d) n = , l = l orbital a) p b) s c) f d) d . . Shapes of Atomic Orbitals The orbital wave function or ψ for an electron in an atom has no physical meaning. It is simply a mathematical function of the coordinates of the electron.
However, for different orbitals the plots of corresponding wave functions as a function of r (the distance from the nucleus) are different. Fig. . (a), gives such plots for s ( n = , l = ) and s ( n = , l = ) orbitals.
of the dots in a region represents electron probability density in that region. Boundary surface diagrams of constant probability density for different orbitals give a fairly good representation of the shapes of the orbitals. In this representation, a boundary surface or contour surface is drawn in space for an orbital on which the value of probability density | ψ | is constant. In principle many such boundary surfaces may be possible.
However, for a given orbital, only that boundary surface diagram of constant probability density * is taken to be good representation of the shape of the orbital which encloses a region or volume in which the probability of finding the electron is very high, say, %. The boundary surface diagram for s and s orbitals are given in Fig. . (b).
One may ask a question : Why do we not draw a boundary surface diagram, which bounds a region in which the probability of finding