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Q17E

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Modern Physics
Found in: Page 134
Modern Physics

Modern Physics

Book edition 2nd Edition
Author(s) Randy Harris
Pages 633 pages
ISBN 9780805303087

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Short Answer

Determine the Compton wavelength of the electron, defined to be the wavelength it would have if its momentum weremec.

Compton Wavelength of the electron

λ=2.43×10-12 m

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :
TABLE OF CONTENTS

Step 1:Given and unknowns.

me=9.1×10-31 kg -- the electron's mass

p=mec -- the electron's momentum

Step 2: Concept Introduction

The following equation can be used to describe the de Broglie wavelength.

p=hλ…………………..(1)

Step 3: Expression of wavelength.

Know that the electron's momentum isp=mec .

Get the wavelength expression as follows

p=hλ

p=mec

mec=hλ

λ=hmec

Step 3: Compton Wavelength of Electron.

Using the wavelength's derived expression, Obtainλ as:

λ=hmec=6.626×10-34 J⋅s(9.1×10-31 kg)×(3.0×108 m/s)=2.43×10-12 m λ=hmec=6.626×10-34 J⋅s(9.1×10-31 kg)×(3.0×108 m/s)=2.43×10-12 m

The Compton Wavelength of the electron isλ=2.43×10-12 m .

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