Chapter 7.3, Problem 7.5BFP

Interpretation Introduction

Interpretation:

The uncertainty in the position of a neutron with mass $1.67\times {10}^{-27}\text{ kg}$ and speed $8\times {10}^7\text{ m/s}\pm 1.00\text{ \%}$ is to be determined.

Concept introduction:

Heisenberg’s uncertainty principle – The Heisenberg’s uncertainty principle states that it is not possible to exactly determine both the position and the momentum for a small moving particle at the same time.

The expression for the uncertainty principle is as follows:

$\left(\Delta x\right)\left(m\Delta u\right)\ge \frac{h}{4\pi }$        (1)

Here,

$\Delta x$ is the uncertainty in the position.

$m$ is the mass.

$\Delta u$ is the uncertainty in the velocity.

$h$ is the Plank’s constant.