EBK EXPLORING CHEMICAL ANALYSIS
EBK EXPLORING CHEMICAL ANALYSIS
5th Edition
ISBN: 8220101443908
Author: Harris
Publisher: MAC HIGHER
Question
Book Icon
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.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
I would like my graphs checked please. Do they look right? Do I have iodine and persulfate on the right axis ?
Reaction Fill-ins Part 2! Predict the product(s) OR starting material of the following reactions. Remember, Hydride shifts are possible if/when a more stable carbocation can exist (depending on reaction mechanism)! Put your answers in the indicated boxes d. d. ง HCI
A cylinder contains 12 L of water vapour at 150˚C and 5 atm. The temperature of the water vapour is raised to 175˚C, and the volume of the cylinder is reduced to 8.5 L. What is the final pressure of the gas in atmospheres? assume that the gas is ideal
Knowledge Booster
Background pattern image
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Chemistry
Chemistry
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Cengage Learning
Text book image
Chemistry
Chemistry
ISBN:9781259911156
Author:Raymond Chang Dr., Jason Overby Professor
Publisher:McGraw-Hill Education
Text book image
Principles of Instrumental Analysis
Chemistry
ISBN:9781305577213
Author:Douglas A. Skoog, F. James Holler, Stanley R. Crouch
Publisher:Cengage Learning
Text book image
Organic Chemistry
Chemistry
ISBN:9780078021558
Author:Janice Gorzynski Smith Dr.
Publisher:McGraw-Hill Education
Text book image
Chemistry: Principles and Reactions
Chemistry
ISBN:9781305079373
Author:William L. Masterton, Cecile N. Hurley
Publisher:Cengage Learning
Text book image
Elementary Principles of Chemical Processes, Bind...
Chemistry
ISBN:9781118431221
Author:Richard M. Felder, Ronald W. Rousseau, Lisa G. Bullard
Publisher:WILEY