Chapter 6.6, Problem 1PPB

Interpretation Introduction

Interpretation:

The minimum uncertainty in momentum and minimum uncertainty in velocity for the atomic particles like neutrons and electrons is to be determined.

Concept Introduction:

The principle that helps to locate any subatomic particle behaving as a wave is called Heisenberg’s Uncertainty Principle.

The equation of Heisenberg’s Uncertainty Principle is as:

$\Delta x.\Delta p\ge \frac{h}{4\pi }.$

Here, $\Delta x$ is the minimum uncertainty in position, $h$ is Planck’s constant, and $\Delta p$ is the minimum uncertainty of momentum.

The expression for the minimum uncertainty of momentum is as:

$\Delta p=m\Delta u.$

Here, $m$ is the mass of particle and $\Delta u$ is the uncertainty in velocity.

The relationship between meters and angstrom can be expressed as:

$\text{1}\text{m}\text{=}{\text{10}}^{10}\stackrel{\text{ο}}{\text{A}}.$

To convert angstromto meters, conversion factor is $\left(\frac{{10}^{-10}\text{m}}{1\stackrel{\text{ο}}{\text{A}}}\right)$.

The relationship between $\text{amu}$ and kilograms can be expressed as:

$1\text{amu}=1.66\times {10}^{-27}\text{kg}\text{.}$

To convert $\text{amu}$ to kilograms, conversion factor is $\frac{1.66\times {10}^{-27}\text{kg}}{\text{1 amu}}.$