From the orbitals, wavefunctions can be constructed using equation (6.2). The square of the wavefunction gives the probability of finding electrons in the corresponding volume elements.
gives the probability of finding electron 1 in volume element
at r1 and electron 2 in volume element
at r2. Since atoms are spherically symmetrical, it is better to consider the radial probability density
where is the probability density of finding any one electron at r . The plot for lithium atom is shown below.
Figure 6.3 Radial probability distribution in Li atom
The Lithium atom has a configuration 1s2 2s1. The 1s electrons lie closer to the nucleus than the 2s electrons. The inner orbitals are held more “tightly” and the outer electrons are more diffuse. The reason is not difficult to find! The outer electrons experience much smaller effective charge due to the shielding of the nuclear charge by the inner or “core” electrons. The radial probability density (radial charge density, e ) also gives an indication about the size of an atom. For Li, we notice that the charge density has become very small beyond 3 Å. This implies that radius of Li, is 3Å. When the outer electron is removed form Li, we get Li+ with an electronic configuration 1s2. The charge density beyond 1 Å would not appear in the scale in figure 6.3 (as the outer electron has been removed) and the Li+ will have a radius less than 1 Å. The experimental radii of Li and Li+ are 3.04 Å and 0.68 Å. The agreement is fairly good. In fact the full charge density curve can be obtained from the scattering experiments on atoms.
gives the probability of finding electron 1 in volume element
at r1 and electron 2 in volume element
at r2. Since atoms are spherically symmetrical, it is better to consider the radial probability density
where 
is the probability density of finding any one electron at r . The plot for lithium atom is shown below. 
