Chapter 6, Problem 25PS

### 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

# Calculate the wavelength, in nanometers, associated with a 46-g golf ball moving at 30. m/s (about 67 mph). At what speed must the ball travel to have a wavelength of 5.6 × 10–3 nm?

Interpretation Introduction

Interpretation: The wavelength of a golf ball moving at 30m/s and the frequency of the golf ball having wavelength 5.6×1012nm 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

Given,

Â Â Massâ€‰ofâ€‰theâ€‰electronâ€‰=â€‰46â€‰gâ€‰=â€‰46â€‰Ã—â€‰10â€‰âˆ’3â€‰kgPlanck'sâ€‰constant,hâ€‰=â€‰6.626â€‰Ã—â€‰10â€‰âˆ’34â€‰J.s

• The wavelength of a golf ball moving at 30â€‰m/s_ is calculated below.

â€‚Â Speedâ€‰ofâ€‰theâ€‰golfÂ ballâ€‰=â€‰30â€‰m/s

According to de Broglieâ€™s equation, wavelength of the golf ball moving at 30â€‰m/s is,

â€‚Â Î»â€‰=â€‰hmv

Substituting the values

â€‚Â Î»â€‰=â€‰6.626â€‰Ã—â€‰10â€‰âˆ’34â€‰J.s46â€‰Ã—â€‰10â€‰âˆ’3â€‰kgâ€‰Ã—â€‰30â€‰m/sâ€‰â€‰=â€‰4.8â€‰Ã—10â€‰âˆ’34â€‰mâ€‰Ã—â€‰(1â€‰Ã—â€‰109â€‰nm/m)=â€‰4.8â€‰Ã—10â€‰âˆ’25â€‰â€‰nm

The wavelength of a golf ball moving at 30â€‰m/s is â€‰4.8â€‰Ã—10â€‰-25â€‰â€‰nm

• The frequency of the golf ball having wavelength 5.6â€‰Ã—10â€‰âˆ’12â€‰â€‰nm_ is calculated below

The wavelength of a golf ball is,

â€‚Â Wavelengthâ€‰ofâ€‰theÂ golfâ€‰ballâ€‰=â€‰5

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started