# Electrons, the nucleus and the uncertainty principle.

by uranium_235
Tags: electrons, nucleus, principle, uncertainty
 P: 36 I read somewhere that one of the explanations for an electron not spiraling into the nucleus is due to the uncertainty principle. If an electron falls into the nucleus both its position and velocity will be certain. How is that possible? Does the nucleus have both certainty in position and velocity? Then would not this explanation contradict its self?
Emeritus
PF Gold
P: 29,238
 Quote by uranium_235 I read somewhere that one of the explanations for an electron not spiraling into the nucleus is due to the uncertainty principle. If an electron falls into the nucleus both its position and velocity will be certain. How is that possible? Does the nucleus have both certainty in position and velocity? Then would not this explanation contradict its self?
1. In a sketch, draw a horizontal axis as the r (radial) axis, and the vertical axis as the potential energy (U) axis.

2. Sketch the coulomb potential U=-kQq/r, where Q is the charge of the nucleus, and q is the charge of another charged particle. This is the potential relevant in a simple, hydrogenic-type atom.

3. For a bound charge particle q, it can have a substantial probability to exist confined within the potential well bounded by the vertical axis, and the U potential profile.

4.. Now look at what happens when a charge q gets closer and closer to the nucleus, i.e. as r -> 0. The particle cannot have a substantial probability anywhere else other than within the potential well. And the width of the well is getting smaller and smaller as r approaches zero, meaning we are confining the charge to smaller and smaller region of space. Consequently, we are knowing more and more about where q is radially, thus reducing the uncertainty in its position.

5. If there is no uncertainty principle, this will cause no problem. However, because it is there, there will be an increase in the range of momentum values the charge can have. This will act as a counter effect to oppose being confined to a smaller volume. Thus, there is a minimum ground state that does not allow it to be any "closer".

Zz.