   Chapter 6, Problem 25PS

Chapter
Section
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,

Massoftheelectron=46g=46×103kgPlanck'sconstant,h=6.626×1034J.s

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

Speedofthegolf ball=30m/s

According to de Broglie’s equation, wavelength of the golf ball moving at 30m/s is,

λ=hmv

Substituting the values

λ=6.626×1034J.s46×103kg×30m/s=4.8×1034m×(1×109nm/m)=4.8×1025nm

The wavelength of a golf ball moving at 30m/s is 4.8×10-25nm

• The frequency of the golf ball having wavelength 5.6×1012nm_ is calculated below

The wavelength of a golf ball is,

Wavelengthofthe golfball=5

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