The Foundations of Chemistry

principal shells (main energy levels) by using the principal quantum number as a coeffi-

cient; 1sindicates the sorbital in the first shell, 2sis the sorbital in the second shell, 2p

is a porbital in the second shell, and so on (Table 5-4).

For each solution to the quantum mechanical equation, we can calculate the electron

probability density (sometimes just called the electron density) at each point in the atom.

This is the probability of finding an electron at that point. It can be shown that this elec-

tron density is proportional to r^2

2 , where ris the distance from the nucleus.

In the graphs in Figure 5-20, the electron probability density at a given distance from

the nucleus is plotted against distance from the nucleus, for sorbitals. It is found that the

electron probability density curve is the same regardless of the direction in the atom. We

Figure 5-19 An electron cloud surrounding an atomic nucleus. The electron density drops

off rapidly but smoothly as distance from the nucleus increases.

z

y

x

Figure 5-20 Plots of the electron density distributions associated with sorbitals. For any

sorbital, this plot is the same in any direction (spherically symmetrical). The sketch below

each plot shows a cross-section, in the plane of the atomic nucleus, of the electron cloud

associated with that orbital. Electron density is proportional to r^2

2.

r^2 

 2

r^2 

 2

radius radius radius

r^2 

 2

 = 0

ls

 = 0

2 s


 = 0

3 s