refers to orientation of the spin of the electron. According to the German physicist, Max Born, the square of the wave function (i.e., ψ ) at a point gives the probability density of the electron at that point. The variation of ψ as a function of r for s and s orbitals is given in Fig. .
(b). Here again, you may note that the curves for s and s orbitals are different. It may be noted that for s orbital the probability density is maximum at the nucleus and it decreases sharply as we move away from it. On the other hand, for s orbital the probability density first decreases sharply to zero and again starts increasing.
After reaching a small maxima it decreases again and approaches zero as the value of r increases further. The region where this probability density function reduces to zero is called nodal surfaces or simply nodes . In general, it has been found that ns -orbital has ( n – ) nodes, that is, number of nodes increases with increase of principal quantum number n . In other words, number of nodes for s orbital is one, two for s and so on.
These probability density variation can be visualised in terms of charge cloud diagrams [Fig. . (a)]. In these diagrams, the density Fig.
. The plots of (a) the orbital wave function ψ(r); (b) the variation of probability density ψ (r) as a function of distance r of the electron from the nucleus for 1s and 2s orbitals. Problem . What is the total number of orbitals associated with the principal quantum number n = ?
For n = , the possible values of l are , and . Thus there is one s orbital ( n = , l = and m l = ); there are three p orbitals ( n = , l = and m l = – , , + ); there are five d orbitals ( n = , l =