A proton is confined within an atomic nucleus of diameter 4 fm(1 fm=10^-15 m) . Estimate the unc

step 1 In this exercise, we're going to talk about Heisenberg's uncertainty principle. So remember that

A proton is confined within an atomic nucleus of diameter 4...

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Key Concepts

Quantum Confinement

Quantum confinement refers to the phenomenon where a particle is restricted to a small spatial region, which in turn leads to a significant increase in the uncertainty of its momentum. When a proton is confined within the tiny dimensions of a nucleus, its position is well-defined, hence its momentum—and consequently its speed—must be highly uncertain.

Momentum-Velocity Relationship

In non-relativistic physics, momentum is directly related to velocity by the relation p = mv. Thus, the uncertainty in a particle's momentum (?p), derived from the uncertainty principle, can be translated into an uncertainty in its speed (?v) using the particle's mass. This connection is essential for estimating the speed uncertainty when a particle is confined.

Heisenberg Uncertainty Principle

This fundamental principle in quantum mechanics asserts that the more precisely a particle's position is known, the less precisely its momentum can be known, and vice versa. It is mathematically expressed as ?x ?p ? ?/2, where ?x represents the uncertainty in position and ?p the uncertainty in momentum.

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