Question #77212

Discuss the vector nature of orbital angular momentum of an electron of the hydrogen

atom.

atom.

Expert's answer

The simplest classical model of the hydrogen atom is one in which the electron moves in a circular planar orbit about the nucleus. 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. The magnitude of the angular momentum is quantized. Secondly, quantum mechanics states that the component of M along a given axis can assume only (2l + 1) values, rather than the infinite number allowed in the classical model.

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. The magnitude of the angular momentum is quantized. Secondly, quantum mechanics states that the component of M along a given axis can assume only (2l + 1) values, rather than the infinite number allowed in the classical model.

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