Question

Relation between angular momentum and radius of a hydrogen atom

Answer 1

The simplest classical model of the hydrogen atom is one in which the electron moves in a circular planar orbit about the nucleus as previously discussed and as illustrated in Fig. 3-7. The angular momentum vector M in this figure is shown at an angle q with respect to some arbitrary axis in space. Assuming for the moment that we can somehow physically define such an axis, then in the classical model of the atom there should be an infinite number of values possible for the component of the angular momentum vector along this axis. As the angle between the axis and the vector M varies continuously from 0°, through 90° to 180°, the component of M along the axis would vary correspondingly from M to zero to -M. Thus the quantum mechanical statements regarding the angular momentum of an electron in an atom differ from the classical predictions in two startling ways. First, the magnitude of the angular momentum (the length of the vector M) is restricted to only certain values given by: