   Chapter 6, Problem 24PS

Chapter
Section
Textbook Problem

A beam of electrons (m = 9.11 X 10–31 kg/electron) has an average speed of 1.3 X 108 m/s. What is the wavelength of electrons having this average speed?

Interpretation Introduction

Interpretation: The wavelength associated with an electron has to be calculated.

Concept introduction:

The de Broglie’s equation is used to relate the wavelength to mass of a particle and the velocity at which it moves.

λ=hmvwhere, h=Planck'sconstantλ=wavelengthm=massoftheparticlev=velocityatwhichtheparticlemoves

Explanation

The wavelength associated with an electron is calculated below.

Given,

Massoftheelectron=9.11×1031kgPlanck'sconstant,h=6.626×1034J.sAverage speedoftheelectron, v=1.3×108m/s

According to de Broglie’s equation, wavelength associated with an electron is,

λ=hmv

Substituting the values,

λ=6.626×1034J

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