   Chapter 6.4, Problem 6.5CYU

Chapter
Section
Textbook Problem

Calculate the wavelength associated with a neutron having a mass of 1.675 x 10‒24 g and a kinetic energy of 6.21 x 10‒21 j. (The kinetic energy of a moving particle is E = 1/2mv2.)

Interpretation Introduction

Interpretation: The wavelength has to be calculated.

Concept introduction:

The de Broglie’s equation is used to relate the wavelength, mass of a particle and the velocity at which it moves.

λ=hmvwhere, h=Planck'sconstantλ=wavelengthm=massoftheparticlev=velocityatwhichtheparticlemoves

Kinetic energy of the moving particle is E=12mv2

Explanation

The wavelength associated with a neutron is calculated below.

Given,

Massoftheneutron=1.675×1024g=1.675×1027kgh=6.626×1034J.sKinetic eneregy oftheneutron=6.21×1021J

Kinetic energy of the moving particle is E=12mv2

Therefore,

Velocity of neutron,v=[2Em]1/2=[2×(6.21×1021)J1.675×1027kg]1/2=2723m

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