Chapter 7, Problem 7.40QP

Interpretation Introduction

Interpretation:

The wavelength (in nanometers) associated with a proton moving at $\text{2}{\text{.90 × 10}}^{\text{8}}\text{ m/s}$ in which mass of the proton is $\text{1}{\text{.673 × 10}}^{-\text{27}}\text{ kg}$ should be calculated using the concept of De Broglie’s hypothesis.

Concept Introduction:

De Broglie’s hypothesis explains the behaviour of waves.  Waves behave like particles whereas particles can behave like wave.  De Broglie derived the equation in which the particle and wave properties are related:

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

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

To find: Calculate the wavelength (in nanometers) associated with a proton moving at $\text{2}{\text{.90 × 10}}^{\text{8}}\text{ m/s}$ in which mass of the proton is $\text{1}{\text{.673 × 10}}^{-\text{27}}\text{ kg}$