It may have been supposed that the average value for the radius of the fi rst orbit in a hydrogen atom
should evaluate to 0.529 Å. The answer to why it does not lies in the fact that the probability of fi nd-
ing the electron as a function of distance from the nucleus in a hydrogen atom can be represented as
shown in Figure 2.1 . The average distance is that point where there is an equal probability of fi nding
the electron on either side of that distance. It is that distance that we have just calculated by the fore-
going procedure. On the other hand, the probability as a function of distance is represented by a func-
tion that goes through a maximum. Where the probability function has its maximum value is the most
probable distance, and that distance for an electron in the 1 s state of a hydrogen atom is a o .