Using the heisenberg's uncertainty principle, can you prove that electron can never exist in nucleus?

Question

In quantum physics, the Heisenberg uncertainty principle is a mathematical limit on the accuracy with which it is possible to measure everything there is to know about a physical system. In its simplest form, it applies to the position and momentum of a single particle, and implies that if we continue increasing the accuracy with which one of these is measured, there will come a point at which the other must be measured with less accuracy. Mathematically, if Δx and Δp are the uncertainties in the measurements of the position and momentum, then the product ΔxΔp is at least on the order of Planck's constant. Stated with more mathematical rigor, the uncertainty principle states that when measuring conjugate quantities, the product of their standard deviations must be at least h/2pi.

Answer 1

Using Heisenberg's principle of uncertainty, one can easily estimate a lower boundary for the kinetic energy of an electron when localized inside a nucleus, since the kinetic Energy is proportional to Δp squared if the electron is confined. You'll get a immense high energy, and you could say that it's impossible for an nucleus to generate an even higher confinement potential to keep such an high energetic electron in place comparing it to the magnitude of Coulomb interaction between charged particles.

But that's just a hand waving line of reasoning, because at these small scales other interactions enter the picture, namely strong and weak interactions. And in fact: The opposite process happens in nature: A free neutron is an unstable particle and decays into a proton, an electron and an electron neutrino with a mean lifetime of approx. 15 minutes.

Answer 2

Heisenberg Uncertainty Principle Proof

Answer 3

I wouldn't say that you could prove an electron can never exist. If you are measuring either position or momentum, obviously there must be mass, and hence a particle. However, you can measure the position with such high accuracy, that your values for momentum (mass and velocity) become very poor, but still exist.

Answer 4

This principle applies to what we can know based on our facilities for which to measure. You can not equate our limited intellect of the created with that of the limitless intellect and power of the creator. We knew nothing 150 years ago about the simple cell and all of its inner workings but today with high tech microscopes we can see that in each cell is a whole entire world of systems maintained by these very small molecular machines. How can we predict, control or affect any particle let alone subatomic yet we try to assume their existence and name and classify them based on limited information and then apply those limits to the God that created all matter to begin with. How ostentatious of you.

Answer 5

Δx *Δv=h/4πm

as Δx is 10^-15m
finding values of velocity

we get 5 x 10^10 m/s as this value is very high and highest velocity is of light so this uncertainity is very high so electron can't be found in nucleus

Answer 6

we know that size of nucleus is in order of 10^-15 m
hence if electron is present in nucleus then you know its position with very high certainity in order of 10^-15
according to relativity velocity of any particle can not be greater than that of light that is its velocity will lie between 0 and3*10^8m/s hence this is maximum uncertainity of any particle
Now use heisenberg's principle you will find thes values do not match

Answer 7

I'm not sure.