Exploring Chemical Analysis
Exploring Chemical Analysis
5th Edition
ISBN: 9781429275033
Author: Daniel C. Harris
Publisher: Macmillan Higher Education
Question
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Chapter 18, Problem 18.9P

(a)

Interpretation Introduction

Interpretation:

Frequency, wavenumber and energy (J/photon and kJ/mol) of photon with 250 nm have to be calculated.

Concept Introduction:

Planck’s hypothesis states energy associated with photon is as follows:

  E=hcλ

Here,

λ denotes wavelength.

h denotes Planck’s constant

c denotes speed of light.

(a)

Expert Solution
Check Mark

Explanation of Solution

Conversion factor to convert nm to m is as follows:

  1 nm=109 m

Thus, 250 nm is converted to m as follows:

  Wavelength=(250 nm)(109 m1 nm)=2.5×107 m

Formula to calculate frequency is as follows:

  v=cλ        (1)

Substitute 2.5×107 m for λ , and 3×108 m/s for c in equation (1).

  v=3×108 m/s2.5×107 m=1.2×1015 Hz

Formula to calculate wavenumber is as follows:

  v¯=vc        (2)

Substitute 1.2×1015 Hz for v , and 3×108 m/s for c in equation (2).

  v¯=(1.2×1015 Hz3×108 m/s)(1 m102 cm)=4.0×104 cm1

Planck’s hypothesis states energy associated with single photon is as follows:

  E=hcλ        (3)

Substitute 2.5×107 m for λ , 6.626×1034 J s for h and 3×108 m/s for c in equation (3).

  E=(6.626×1034 J s)(3×108 m/s)(2.5×107 m)=7.95×1019 J/photon

Avogadro’s number is 6.022×1023 photons/mol. So energy for 1 mol photons is calculated as follows:

  E=(6.022×1023 photons/mol)(7.95×1019 J1 photon)(1 kJ1000 J)=478.7 kJ/mol479 kJ/mol

Thus, frequency, wavenumber and energy (J/photon and kJ/mol) are 1.2×1015 Hz, 4.0×103 cm1, 7.95×1019 J/photon and 479 kJ/mol respectively.

(b)

Interpretation Introduction

Interpretation:

Frequency, wavenumber and energy (J/photon and kJ/mol) of photon with 2.50 μm have to be calculated.

Concept Introduction:

Refer to part (a).

(b)

Expert Solution
Check Mark

Explanation of Solution

Conversion factor to convert μm to m is as follows:

  1 μm=106 m

Thus, 2.50 μm is converted to m as follows:

  Wavelength=(2.50 μm)(106 m1 μm)=2.5×106 m

Substitute 2.5×106 m for λ , and 3×108 m/s for c in equation (1).

  v=3×108 m/s2.5×106 m=1.2×1014 Hz

Substitute 1.2×1014 Hz for v , and 3×108 m/s for c in equation (2).

  v¯=(1.2×1014 Hz3×108 m/s)(1 m102 cm)=4.0×103 cm1

Substitute 2.5×106 m for λ , 6.626×1034 J s for h and 3×108 m/s for c in equation (3).

  E=(6.626×1034 J s)(3×108 m/s)(2.5×106 m)=7.95×1020 J/photon

Avogadro’s number is 6.022×1023 photons/mol. So energy for 1 mol photons is calculated as follows:

  E=(6.022×1023 photons/mol)(7.95×1020 J1 photon)(1 kJ1000 J)=47.87 kJ/mol47.9 kJ/mol

Thus, frequency, wavenumber and energy (J/photon and kJ/mol) are 1.2×1014 Hz, 4.0×103 cm1, 7.95×1020 J/photon and 47.9 kJ/mol respectively.

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