Chapter 3.6, Problem 3.6.1SR

Interpretation Introduction

Interpretation:

The minimum speed required for a hydrogen atom to have a de Broglie wavelength in the ultraviolet region ($\text{10 – 400 nm}$) of the electromagnetic spectrum should be calculated 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 calculate: Calculate the minimum speed required for a hydrogen atom to have a de Broglie wavelength in the ultraviolet region of $\text{10 – 400 nm}$