   # Which of the following particles has the longest wavelength? a an electron traveling at x meters per second b a proton traveling at x meters per second c a proton traveling at 2 x meters per second ### General Chemistry - Standalone boo...

11th Edition
Steven D. Gammon + 7 others
Publisher: Cengage Learning
ISBN: 9781305580343

#### Solutions

Chapter
Section ### General Chemistry - Standalone boo...

11th Edition
Steven D. Gammon + 7 others
Publisher: Cengage Learning
ISBN: 9781305580343
Chapter 7, Problem 7.31QP
Textbook Problem
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## Which of the following particles has the longest wavelength? a an electron traveling at x meters per second b a proton traveling at x meters per second c a proton traveling at 2x meters per second

Interpretation Introduction

Interpretation:

From the given particles, the particle with longest wavelength has to be identified.

Concept introduction:

Louis de Broglie in 1923 rationalized that when light shows particle aspects, then particles of matter display properties of waves under definite circumstances.

λ=h

h is Planck’s constant( 6.63×10-34J.s ) which relates energy and frequency.

υ is the speed of particle.

m is the mass of particle.

λ is the wavelength.

The above equation is called de Broglie relation.

### Explanation of Solution

Reason for correct option:

To identify: The particle with longest wavelength.

The weight of proton is 2000 times greater than electron weight.  It is clear from de Broglie relation, the relationship between wavelength and speed and mass is inverse proportion.  Among the given options, option b and c get rejected because they are protons and their mass is greater than electrons which results in shortest wavelength

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