OWLv2 for Moore/Stanitski's Chemistry: The Molecular Science, 5th Edition, [Instant Access], 1 term (6 months)
OWLv2 for Moore/Stanitski's Chemistry: The Molecular Science, 5th Edition, [Instant Access], 1 term (6 months)
5th Edition
ISBN: 9781285460420
Author: John W. Moore; Conrad L. Stanitski
Publisher: Cengage Learning US
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Chapter 9, Problem 71QRT
Interpretation Introduction

Interpretation:

The maximum wavelength of the radiation that would be diffracted by NaCl crystal has to be determined.  The frequency of radiation and the energy associated with one photon and one mole of photons of the radiation have to be calculated.  This radiation belongs to which region of the spectrum has to be determined.

Concept Introduction:

The maximum wavelength of the radiation that would be diffracted by a crystal is equal to its unit cell edge length.

Electromagnetic radiation consists of oscillating, perpendicular electric and magnetic fields that travel through space at the same rate.  The frequency of electromagnetic radiation is related to its wavelength by equation as given below.

  νλ=c

Where, ν= Frequency of electromagnetic radiation, λ= Wavelength of electromagnetic radiation and c= Velocity of light.

The energy of radiation is proportional to its frequency of radiation according to the equation as given below.

  E=hν

Where, h= Planck’s constant =6.626×1034Js

Frequency and energy range of electromagnetic radiation:

 Frequency Range (Hz)Energy Range (J)
Gamma rays1020102410141010
X rays1017102010171014
UV1015101710201018
IR1013101410221020
Microwaves3×1011101310251022
Radiowaves<3×101110301025

Expert Solution & Answer
Check Mark

Answer to Problem 71QRT

The frequency of radiation of one photon and one mole photons are found out to be 5.30×1017s-1 and 31.91×1040s-1 respectively.  The energy associated with one photon and one mole of photons are found to be 3.51×10-16J and 2.11×108J respectively.

Explanation of Solution

The maximum wavelength of the radiation that would be diffracted by a crystal is equal to its unit cell edge length.  So λmax for NaCl is 566pm which is the unit cell edge length.

(a) Then, the frequency of radiation can be calculated as given below.

  ν=cλ=2.998×108m/s566pm×1012m1pm=5.30×1017s1.

Therefore, the frequency of radiation of one photon is found out to be 5.30×1017s-1.

The energy associated with one photon can also be calculated as follows,

  E=hν=(6.626×1034Js)×(5.30×1017s1)=3.51×10-16J.

(b) The frequency of radiation of one mole photons can be calculated as follows,

  1molphoton×5.30×1017s-11photon×6.022×1023photons1molphoton=31.91×1040s-1.

The energy associated with one mole photons can also be calculated as follows,

  E=hν=(6.626×1034Js)×(31.91×1040s1)=2.11×108J.

The energy and frequency range are coming under X-ray region of electromagnetic spectrum.

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Chapter 9 Solutions

OWLv2 for Moore/Stanitski's Chemistry: The Molecular Science, 5th Edition, [Instant Access], 1 term (6 months)

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