Chapter 3, Problem 3.129QP

Interpretation Introduction

Interpretation:

The element which has a single atom travelling at $\text{15 percent}$ of the speed of light and having de Broglie wavelength of $\text{1}{\text{.06 × 10}}^{-\text{16}}\text{ m}$ should be found using the concept of De Broglie’s hypothesis.

Concept Introduction:

De Broglie’s hypothesis explains the behaviour of waves.  Waves can behave like particles while particles can exhibit wave like properties.  De Broglie deduced that the particle and wave properties are related by the following expression:

$\text{λ }=\frac{\text{h}}{\text{mu}}$

where, $\text{λ}$ is the wavelength associated with a moving particle; $\text{h}$ is Planck’s constant; $\text{m}$ is the mass of the particle and $\text{u}$ is the velocity of the moving particle.

To find: The element which has a single atom travelling at $\text{15 percent}$ of the speed of light and having de Broglie wavelength of $\text{1}{\text{.06 × 10}}^{-\text{16}}\text{ m}$