Chemistry & Chemical Reactivity
Chemistry & Chemical Reactivity
10th Edition
ISBN: 9781337399074
Author: John C. Kotz, Paul M. Treichel, John Townsend, David Treichel
Publisher: Cengage Learning
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Chapter 6, Problem 57GQ

A cell phone sends signals at about 850 MHz (where 1 MHz = 1 × 106 Hz or cycles per second). (a) What is the wavelength of this radiation? (b) What is the energy of 1.0 mol of photons with a frequency of 850 MHz? (c) Compare the energy in part (b) with the energy of a mole of photons of violet light (420 nm). (d) Comment on the difference in energy between 850 MHz radiation and violet light.

(a)

Expert Solution
Check Mark
Interpretation Introduction

Interpretation: The wavelength of cell phone signal has to be calculated.

Concept introduction:

The frequency of the light is inversely proportional to its wavelength.

  ν=cλwhere, c=speedoflightν=frequencyλ=wavelength

Answer to Problem 57GQ

The wavelength of cell phone signal is 0.35m

Explanation of Solution

The wavelength of phone signal is calculated below.

Given,

The frequency of cell phone signal is 850MHz=850 ×106Hz=850 ×106s1

  The speed of light,c=2.998×108m/s

The wavelength of cell phone signal is calculated by using the equation,

    λ=cν=2.998×108m/s850 ×106s1=0.35m

The wavelength of cell phone signal is 0.35m

(b)

Expert Solution
Check Mark
Interpretation Introduction

Interpretation: The energy per mole of photons of cell phone signal has to be calculated.

Concept introduction:

Planck’s equation,

  E=where, E=energyh=Planck'sconstantν=frequency

The energy increases as the wavelength of the light decrease. Also the energy increases as the frequency of the light increases.

Answer to Problem 57GQ

The energy per mole of photons of cell phone signal is 0.34J/mol

Explanation of Solution

The energy per photon cell phone signal is calculated,

Given,

The frequency of cell phone signal is 850MHz=850 ×106Hz=850 ×106s1

  Planck'sconstant,h=6.626×1034J.sThe speed of light,c=2.998×108m/sAvogadro's number,NA=6.022×1023photons/mol

The energy per photon cell phone signal is calculated,

  E=

Substituting the values to the above equation,

  E==6.626×1034J.s×850 ×106s1=5.6321×1025J

The energy per photon is 5.6321×1025J

The energy per mole of photons of cell phone signal is calculated,

The energy per mole of photons is the product of energy per photon and Avogadro’s number,NA.

Therefore,

The energy per mole of photons of cell phone signal is,

Energy per mole of photon=NA=6.022×1023photons/mol×5.6321×1025J/photon=0.34J/mol

The energy per mole of photons of cell phone signal is 0.34J/mol

(c)

Expert Solution
Check Mark
Interpretation Introduction

Interpretation: The energy of violet light is to be compared with 850MHz cell phone signal

Concept introduction:

  • Planck’s equation,

  E=where, E=energyh=Planck'sconstantν=frequency

The energy increases as the wavelength of the light decrease. Also the energy increases as the frequency of the light increases.

  • The frequency of the light is inversely proportional to its wavelength.

  ν=cλwhere, c=speedoflightν=frequencyλ=wavelength

Answer to Problem 57GQ

The energy per mole of photons of cell phone signal is 0.34J/mol whereas the energy per mole of photons of violet light is 280kJ/mol

Explanation of Solution

Given,

The wavelength violet light is 420nm=4.20 ×107m

  Planck'sconstant,h=6.626×1034J.sThe speed of light,c=2.998×108m/sAvogadro's number,NA=6.022×1023photons/mol

The frequency of violet light is,

    ν=cλ                                        (a)

The energy per photon of violet light is,

  E=                                        (b)

Combining (a) and (b)

    E=hcλ

Substituting the values to the above equation,

  E=hcλ=6.626×1034J.s×2.998×108m/s4.20 ×107m=4.72×1019J

The energy per photon is 4.72×1019J

  • The energy per mole of photons of violet light is calculated,

The energy per mole of photons is the product of energy per photon and Avogadro’s number,NA.

Therefore,

The energy per mole of photons of violet light is,

Energy per mole of photon=NA=6.022×1023photons/mol×4.72×1019J/photons=280kJ/mol

The energy per mole of photons of violet light is 280kJ/mol

The energy per mole of photons of cell phone signal is 0.34J/mol whereas the energy per mole of photons of violet light is 280kJ/mol

(d)

Expert Solution
Check Mark
Interpretation Introduction

Interpretation: The energy difference in violet light and cell phone signal with 850MHz has to be compared.

Concept introduction:

Planck’s equation,

  E=where, E=energyh=Planck'sconstantν=frequency

The energy increases as the wavelength of the light decrease. Also the energy increases as the frequency of the light increases.

Answer to Problem 57GQ

The energy per mole of photons of violet light is 840000 times greater than the energy per mole of photons of cell phone signal.

Explanation of Solution

The energy per mole of photons of cell phone signal is 0.34J/mol whereas the energy per mole of photons of violet light is 280kJ/mol

Hence,

Energy per mole of photons of violet lightEnergy per mole of photons of cell phone signal=280×103J/mol0.34J/mol=823529=820000

Therefore,

The energy per mole of photons of violet light is 820000 times greater than the energy per mole of photons of cell phone signal.

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Chapter 6 Solutions

Chemistry & Chemical Reactivity

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