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Chapter 6.4, Problem 6.5CYU
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### Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074

#### Solutions

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Section
BuyFindarrow_forward

### Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074
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,

Â Â Massâ€‰ofâ€‰theâ€‰neutronâ€‰=â€‰1.675â€‰Ã—â€‰10â€‰âˆ’24â€‰gâ€‰=â€‰1.675â€‰Ã—â€‰10â€‰âˆ’27â€‰kghâ€‰=â€‰6.626â€‰Ã—â€‰10â€‰âˆ’34â€‰J.sKineticÂ eneregyÂ ofâ€‰theâ€‰neutronâ€‰=â€‰6.21â€‰Ã—â€‰10â€‰âˆ’21â€‰J

Kinetic energy of the moving particle is Eâ€‰=â€‰12â€‰mv2

Therefore,

VelocityÂ ofÂ neutron,â€‰vâ€‰=â€‰[2Em]1/2=â€‰[2â€‰Ã—â€‰(6.21â€‰Ã—â€‰10â€‰âˆ’21)â€‰J1.675â€‰Ã—â€‰10â€‰âˆ’27â€‰kg]1/2=â€‰2723â€‰m

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