0

From a text of Richard Feynman:

You know, of course, that atoms are made with positive protons in the nucleus and with electrons outside. You may ask: “If this electrical force is so terrific, why don’t the protons and electrons just get on top of each other? If they want to be in an intimate mixture, why isn’t it still more intimate?” The answer has to do with the quantum effects. If we try to confine our electrons in a region that is very close to the protons, then according to the uncertainty principle they must have some mean square momentum which is larger the more we try to confine them. It is this motion, required by the laws of quantum mechanics, that keeps the electrical attraction from bringing the charges any closer together.

Can someone explain the following part in a bit more clear way?:

"according to the uncertainty principle they must have some mean square momentum which is larger the more we try to confine them"

user16307
  • 169

2 Answers2

0

Well, in the non-mathematical, Heisenberg-type interpretation of the uncertainty principle, the confinement is related to a localization of the particle, i.e. the more confined the particle is, the smaller the $\Delta x$ (mean square deviation in coordinate or precision to measure it) is. Then, the bigger the $\Delta p$ (mean square deviation in momentum) is. But take this with a grain of salt. The interpretation of $\Delta x \Delta p \geq \frac \hbar 2$ is far from unique.

DanielC
  • 4,333
  • Heisenberg historical interpretation was about measurement and the inability to measure both position and momentum precisely. The interpretation you use in your answer is fairly close to the modern one, i.e. the impossibility to prepare quantum states localised in both position and momentum (the Robertson's style to be technical). So I'd say that's very likely what Feynman had in mind. –  Oct 22 '17 at 16:48
0

Can someone explain the following part in a bit more clear way?:

"according to the uncertainty principle they must have some mean square momentum which is larger the more we try to confine them"

He is handwaving using the Heinseberg Uncertainty (HUP). He means that if the electron had a small radius, its ΔxΔp>h/2π would force the momentum to be very large and not allow the electron to fall and rest on the center of positive charge.

Please read my answer here Why can't electrons fall into the nucleus? which uses data to show the necessity of inventing quantum mechanics .The HUP is a consequence of the commutators in quantum mechanics.

Community
  • 1
anna v
  • 233,453
  • Is dx the distance of the electron from the nucleus in this case? – user16307 Oct 22 '17 at 17:26
  • The attraction is the electric field , so r=0 is where the electric field will neutralize, so dx is that distance. by radius I meant radius of an orbit around the nucleus. – anna v Oct 23 '17 at 04:37