# Neutrons and uncertainty principle

• carllacan
In summary, the conversation discusses the use of the Uncertainty Principle to show that neutrons cannot be formed by a proton and an electron. The speaker acknowledges that if this were the case, the two particles would attract each other until their momentums were zero. However, they are unsure of how to show this arithmetically and question the relevance of the Uncertainty Principle in this situation. They also discuss the missing rest mass of 0.782 MeV/c2 and its relation to ΔE. Overall, the question is from a nuclear physics course and there is no specific context provided.
carllacan

## Homework Statement

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

## 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.

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 ?

BvU said:
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?

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

BvU said:
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?

## What are neutrons and how do they relate to the uncertainty principle?

Neutrons are subatomic particles found in the nucleus of an atom. They have a neutral charge and are responsible for the stability of the nucleus. According to the uncertainty principle, it is impossible to know the precise location and momentum of a neutron at the same time. This is due to the wave-particle duality of quantum mechanics.

## How does the uncertainty principle impact our understanding of neutrons?

The uncertainty principle states that the more precisely we know the position of a neutron, the less we know about its momentum and vice versa. This means that our understanding of neutrons is limited by this principle, as it is impossible to know both properties simultaneously.

## Can we measure the position and momentum of a neutron at the same time?

No, due to the uncertainty principle, it is impossible to measure both the position and momentum of a neutron at the same time. This is a fundamental limitation of quantum mechanics and has been confirmed through numerous experiments.

## How does the uncertainty principle affect the behavior of neutrons?

The uncertainty principle affects the behavior of neutrons by imposing limits on our ability to predict their position and momentum. This means that the behavior of neutrons is inherently probabilistic, and we can only make predictions about their behavior within a certain range of uncertainty.

## Is the uncertainty principle specific to neutrons or does it apply to all particles?

The uncertainty principle applies to all particles, not just neutrons. It is a fundamental principle of quantum mechanics that governs the behavior of all subatomic particles. However, the extent to which the uncertainty principle affects different particles may vary depending on their properties and interactions.

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