Application Of Uncertainty

Introduction:

The uncertainty principle has far reaching implications. In fact, it has been very useful in explaining many observations which cannot be explained otherwise.

Application:

An important one being the proof of the non-existence of an electron inside the nucleus. In beta decay, the electrons are emitted from the nucleus of the radioactive element. The radius of a typical atomic nucleus to be about  5.0 × 10⁻¹⁵ m. Assuming that the uncertainty in the position of the electron inside the nucleus to be of the same order, we have

If this is the uncertainty in a nuclear electron’s momentum p itself must be at least comparable in magnitude. An electron with such a momentum has a kinetic energy, KE, many times greater than its rest energy (which is mc²). The kinetic energy of such particle is given by

This means that the kinetic energy of an electron must exceed 20MeV if it is to be inside a nucleus. Experiments show that the electrons emitted by certain unstable nuclei never have more than a small fraction of this energy, from which we conclude that nuclei cannot contain electrons. The electron that an unstable nucleus may emit comes into being only at the moment the nucleus decays.