Chapter 6, Problem 26PS

### 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

# A rifle bullet (mass = 1.50 g) has a velocity of 7.00 x 102 mph (miles per hour). What is the wavelength associated with this bullet?

Interpretation Introduction

Interpretation: The wavelength of the rifle bullet is 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 of the rifle bullet is calculated below.

Given,

Â Â Massâ€‰ofâ€‰theâ€‰bulletâ€‰=â€‰1.50â€‰gâ€‰=â€‰1.50â€‰Ã—â€‰10â€‰âˆ’3â€‰kgPlanck'sâ€‰constant,hâ€‰=â€‰6.626â€‰Ã—â€‰10â€‰âˆ’34â€‰J.sVelocityâ€‰ofâ€‰theâ€‰bullet,Â vâ€‰=â€‰7.00â€‰Ã—â€‰102â€‰milesÂ perÂ hour=â€‰7.00â€‰Ã—â€‰102â€‰milesÂ perÂ hourÃ—â€‰1609.34â€‰m3600â€‰s=â€‰312.927â€‰m/sâ€‰

According to de Broglieâ€™s equation, wavelength of the rifle bullet is,

â€‚Â Î»â€‰=â€‰hmv

Substituting the values,

â€‚Â Î»â€‰=â€‰6

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