Neutrons and uncertainty principle

[carllacan]

Homework Statement

Using the Uncertainty Principle show arithmetically that neutrons can't be formed by a proton and an electron.

Homework Equations

The Attempt at a Solution

I can see that if neutrons were made out of a proton and an electron they would just attract each until they were together, and after that their momentums would be 0 and we could also know their position, by I don't know how to show it arithmetically.

 

[BvU]

Uncertainy principle doesn't sound like doing a momentum balance.
What is the context of this exercise ? I mean, from the rest masses you miss 0.782 MeV/c², so ΔEΔt > h/4π leaves you with a very short Δt, but who says the electron can't be shot at the proton with a hefty kinetic energy ?

 

[carllacan]

Uncertainy principle doesn't sound like doing a momentum balance.
What is the context of this exercise ? I mean, from the rest masses you miss 0.782 MeV/c², so ΔEΔt > h/4π leaves you with a very short Δt, but who says the electron can't be shot at the proton with a hefty kinetic energy ?

There is no context, that is the whole question. Its on a nuclear physics course, if that helps.

What do you mean yu miss 0.782 MeV/c² from the masses?

 

[BvU]

if you look up p, n, e rest mass and calculate the difference n - p - e

 

[carllacan]

if you look up p, n, e rest mass and calculate the difference n - p - e

Ah, I see. And that difference is related to ΔE?