Chapter 6, Problem 23PS

Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074

Chapter
Section

Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074
Textbook Problem

An electron moves with a velocity of 2.5 X 108 cm/s. What is its wavelength?

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,

Â Â Massâ€‰ofâ€‰theâ€‰electronâ€‰â€‰=â€‰9.11â€‰Ã—â€‰10â€‰âˆ’31â€‰kgPlanck'sâ€‰constant,hâ€‰=â€‰6.626â€‰Ã—â€‰10â€‰âˆ’34â€‰J.sVelocityâ€‰ofâ€‰theâ€‰electron,Â vâ€‰=â€‰2.5â€‰Ã—â€‰10â€‰8â€‰cm/s=â€‰2.5â€‰Ã—â€‰106â€‰m/sâ€‰

According to de Broglieâ€™s equation, wavelength associated with an electron is,

â€‚Â Î»â€‰=â€‰hmv=â€‰6.626â€‰Ã—â€‰10â€‰âˆ’34â€‰J.s9.11â€‰Ã—â€‰10â€‰âˆ’31â€‰kgâ€‰Ã—â€‰2.5â€‰Ã—â€‰106â€‰m/sâ€‰â€‰=â€‰2

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