Atkins' Physical Chemistry
Atkins' Physical Chemistry
11th Edition
ISBN: 9780198769866
Author: ATKINS, P. W. (peter William), De Paula, Julio, Keeler, JAMES
Publisher: Oxford University Press
bartleby

Concept explainers

Question
Book Icon
Chapter 11, Problem 11A.1AE

(i)

Interpretation Introduction

Interpretation:

The ratio A/B for transitions with 70.8pm X-rays has to be calculated.

Concept introduction:

Emission is defined as the release of energy or gas into the environment.  During emission, the transfer of energy from one radioactive substance to the other takes place.  The electron gets excited from ground state to the excited state when small amount of energy is transferred and emits electromagnetic energy when it comes back.  The formula to calculate the ratio A/B for transition is given below.

    AB=8πhv3c3

(i)

Expert Solution
Check Mark

Answer to Problem 11A.1AE

The ratio of A/B for transitions with 70.8pm X-rays is 0.0468Jsm3_.

Explanation of Solution

The formula to calculate the ratio A/B for transition is given below.

    AB=8πhv3c3        (1)

Where,

  • A is the Einstein’s coefficient of spontaneous emission.
  • B is the Einstein’s coefficient of stimulated emission.
  • h is the Planck’s constant
  • v is the frequency of the given radiation.
  • c is the speed of light.

The formula to calculate frequency is given by the expression as shown below.

    v=cλ        (2)

Where,

  • c is the speed of light.
  • λ is the wavelength.

Substitute the value of v in the equation (1).

    AB=8πhv3c3AB=8πhλ3        (3)

The given value of wavelength is 70.8pm.

The conversion of pm into m is done as shown below.

    1pm=1012m

Therefore, the conversion of 70.8pm into m is as follows.

    1pm=1012m70.8pm=70.8×1012m

Substitute the value of λ in the equation (3).

    AB=8πhλ3=8×3.14×(6.625×1034Js)(70.8×1012m)3=0.0468Jsm3_

Therefore, the ratio of A/B for transitions with 70.8pm X-rays is 0.0468Jsm3_.

(ii)

Interpretation Introduction

Interpretation:

The ratio A/B for transitions with 500nm visible light has to be calculated.

Concept introduction:

Emission is defined as the release of energy or gas into the environment.  During emission, the transfer of energy from one radioactive substance to the other takes place.  The electron gets excited from ground state to the excited state when small amount of energy is transferred and emits electromagnetic energy when it comes back.  The formula to calculate the ratio A/B for transition is given below.

    AB=8πhv3c3

(ii)

Expert Solution
Check Mark

Answer to Problem 11A.1AE

The ratio A/B for transitions with 500nm visible light is 1.33×1013Jsm3_.

Explanation of Solution

The formula to calculate the ratio A/B for transition is given below.

    AB=8πhv3c3        (1)

Where,

  • A is the Einstein’s coefficient of spontaneous emission.
  • B is the Einstein’s coefficient of stimulated emission.
  • h is the Planck’s constant
  • v is the frequency of the given radiation.
  • c is the speed of light.

The formula to calculate frequency is given by the expression as shown below.

    v=cλ        (2)

Where,

  • c is the speed of light.
  • λ is the wavelength.

Substitute the value of v in the equation (1).

    AB=8πhv3c3AB=8πhλ3        (3)

The given value of wavelength is 500nm.

The conversion of nm into m is done as shown below.

    1nm=109m

Therefore, the conversion of 500nm into m is as follows.

    1nm=109m500nm=500×109m

Substitute the value of λ in the equation (3).

    AB=8πhλ3=8×3.14×(6.625×1034Js)(500×109m)3=1.33×1013Jsm3_

Therefore, the ratio A/B for transitions with 500nm visible light is 1.33×1013Jsm3_.

(iii)

Interpretation Introduction

Interpretation:

The ratio A/B for transitions with 3000cm1 infrared radiation has to be calculated.

Concept introduction:

Emission is defined as the release of energy or gas into the environment.  During emission, the transfer of energy from one radioactive substance to the other takes place.  The electron gets excited from ground state to the excited state when small amount of energy is transferred and emits electromagnetic energy when it comes back.  The formula to calculate the ratio A/B for transition is given below.

    AB=8πhv3c3

(iii)

Expert Solution
Check Mark

Answer to Problem 11A.1AE

The ratio A/B for transitions with 3000cm1 infrared radiation is 4.5×1028Jsm3_.

Explanation of Solution

The formula to calculate the ratio A/B for transition is given below.

    AB=8πhv3c3        (1)

Where,

  • A is the Einstein’s coefficient of spontaneous emission.
  • B is the Einstein’s coefficient of stimulated emission.
  • h is the Planck’s constant
  • v is the frequency of the given radiation.
  • c is the speed of light.

The formula to calculate frequency is given by the expression as shown below.

    v=cλ        (2)

Where,

  • c is the speed of light.
  • λ is the wavelength.

Substitute the value of v in the equation (1).

    AB=8πhv3c3AB=8πhλ3        (3)

The formula to calculate wave number is given below.

    v¯=1λ

The above equation can be written as shown below.

    λ=1v¯        (4)

Substitute the value of λ in the equation (4).

    AB=8πhv¯3        (5)

The given value of wave number is 3000cm1.

The conversion of cm into m is done as shown below.

    1cm=102m

Therefore, the conversion of 3000cm1 into m is done as shown below.

    1cm=102m3000cm=3000×102m

Substitute the value of wave number in the equation (5).

    AB=8πhv¯3=8×3.14×(6.625×1034Js)×(3000×102m)3=4493.3×1028Jsm34.5×1028Jsm3_

Therefore, the ratio A/B for transitions with 3000cm1 infrared radiation is 4.5×1028Jsm3_.

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!

Chapter 11 Solutions

Atkins' Physical Chemistry

Ch. 11 - Prob. 11E.2STCh. 11 - Prob. 11F.2STCh. 11 - Prob. 11A.1DQCh. 11 - Prob. 11A.2DQCh. 11 - Prob. 11A.3DQCh. 11 - Prob. 11A.1AECh. 11 - Prob. 11A.1BECh. 11 - Prob. 11A.2AECh. 11 - Prob. 11A.2BECh. 11 - Prob. 11A.3AECh. 11 - Prob. 11A.3BECh. 11 - Prob. 11A.4AECh. 11 - Prob. 11A.4BECh. 11 - Prob. 11A.5AECh. 11 - Prob. 11A.5BECh. 11 - Prob. 11A.6AECh. 11 - Prob. 11A.6BECh. 11 - Prob. 11A.7AECh. 11 - Prob. 11A.7BECh. 11 - Prob. 11A.8AECh. 11 - Prob. 11A.8BECh. 11 - Prob. 11A.9AECh. 11 - Prob. 11A.9BECh. 11 - Prob. 11A.10AECh. 11 - Prob. 11A.10BECh. 11 - Prob. 11A.11AECh. 11 - Prob. 11A.11BECh. 11 - Prob. 11A.12AECh. 11 - Prob. 11A.12BECh. 11 - Prob. 11A.1PCh. 11 - Prob. 11A.2PCh. 11 - Prob. 11A.3PCh. 11 - Prob. 11A.4PCh. 11 - Prob. 11A.5PCh. 11 - Prob. 11A.7PCh. 11 - Prob. 11A.8PCh. 11 - Prob. 11A.9PCh. 11 - Prob. 11A.11PCh. 11 - Prob. 11B.1DQCh. 11 - Prob. 11B.2DQCh. 11 - Prob. 11B.3DQCh. 11 - Prob. 11B.4DQCh. 11 - Prob. 11B.5DQCh. 11 - Prob. 11B.6DQCh. 11 - Prob. 11B.7DQCh. 11 - Prob. 11B.8DQCh. 11 - Prob. 11B.1AECh. 11 - Prob. 11B.1BECh. 11 - Prob. 11B.3AECh. 11 - Prob. 11B.3BECh. 11 - Prob. 11B.4BECh. 11 - Prob. 11B.5AECh. 11 - Prob. 11B.5BECh. 11 - Prob. 11B.6AECh. 11 - Prob. 11B.6BECh. 11 - Prob. 11B.7AECh. 11 - Prob. 11B.7BECh. 11 - Prob. 11B.8AECh. 11 - Prob. 11B.8BECh. 11 - Prob. 11B.9AECh. 11 - Prob. 11B.9BECh. 11 - Prob. 11B.10AECh. 11 - Prob. 11B.10BECh. 11 - Prob. 11B.11AECh. 11 - Prob. 11B.11BECh. 11 - Prob. 11B.12AECh. 11 - Prob. 11B.12BECh. 11 - Prob. 11B.13AECh. 11 - Prob. 11B.13BECh. 11 - Prob. 11B.14AECh. 11 - Prob. 11B.14BECh. 11 - Prob. 11B.1PCh. 11 - Prob. 11B.2PCh. 11 - Prob. 11B.3PCh. 11 - Prob. 11B.4PCh. 11 - Prob. 11B.5PCh. 11 - Prob. 11B.6PCh. 11 - Prob. 11B.7PCh. 11 - Prob. 11B.8PCh. 11 - Prob. 11B.9PCh. 11 - Prob. 11B.10PCh. 11 - Prob. 11B.11PCh. 11 - Prob. 11B.12PCh. 11 - Prob. 11B.13PCh. 11 - Prob. 11B.14PCh. 11 - Prob. 11C.1DQCh. 11 - Prob. 11C.2DQCh. 11 - Prob. 11C.3DQCh. 11 - Prob. 11C.4DQCh. 11 - Prob. 11C.1AECh. 11 - Prob. 11C.1BECh. 11 - Prob. 11C.2AECh. 11 - Prob. 11C.2BECh. 11 - Prob. 11C.3AECh. 11 - Prob. 11C.3BECh. 11 - Prob. 11C.4AECh. 11 - Prob. 11C.4BECh. 11 - Prob. 11C.5AECh. 11 - Prob. 11C.5BECh. 11 - Prob. 11C.6AECh. 11 - Prob. 11C.6BECh. 11 - Prob. 11C.7AECh. 11 - Prob. 11C.7BECh. 11 - Prob. 11C.8AECh. 11 - Prob. 11C.8BECh. 11 - Prob. 11C.2PCh. 11 - Prob. 11C.3PCh. 11 - Prob. 11C.4PCh. 11 - Prob. 11C.5PCh. 11 - Prob. 11C.6PCh. 11 - Prob. 11C.7PCh. 11 - Prob. 11C.8PCh. 11 - Prob. 11C.9PCh. 11 - Prob. 11C.10PCh. 11 - Prob. 11C.11PCh. 11 - Prob. 11C.12PCh. 11 - Prob. 11C.13PCh. 11 - Prob. 11C.15PCh. 11 - Prob. 11C.17PCh. 11 - Prob. 11C.18PCh. 11 - Prob. 11C.19PCh. 11 - Prob. 11D.1DQCh. 11 - Prob. 11D.2DQCh. 11 - Prob. 11D.3DQCh. 11 - Prob. 11D.1AECh. 11 - Prob. 11D.1BECh. 11 - Prob. 11D.2AECh. 11 - Prob. 11D.2BECh. 11 - Prob. 11D.3AECh. 11 - Prob. 11D.3BECh. 11 - Prob. 11D.4AECh. 11 - Prob. 11D.4BECh. 11 - Prob. 11D.5AECh. 11 - Prob. 11D.5BECh. 11 - Prob. 11D.6AECh. 11 - Prob. 11D.6BECh. 11 - Prob. 11D.7AECh. 11 - Prob. 11D.7BECh. 11 - Prob. 11D.2PCh. 11 - Prob. 11E.1DQCh. 11 - Prob. 11E.1AECh. 11 - Prob. 11E.1BECh. 11 - Prob. 11E.2AECh. 11 - Prob. 11E.2BECh. 11 - Prob. 11E.3AECh. 11 - Prob. 11E.3BECh. 11 - Prob. 11E.1PCh. 11 - Prob. 11E.2PCh. 11 - Prob. 11F.1DQCh. 11 - Prob. 11F.2DQCh. 11 - Prob. 11F.3DQCh. 11 - Prob. 11F.4DQCh. 11 - Prob. 11F.5DQCh. 11 - Prob. 11F.6DQCh. 11 - Prob. 11F.1AECh. 11 - Prob. 11F.1BECh. 11 - Prob. 11F.2AECh. 11 - Prob. 11F.2BECh. 11 - Prob. 11F.3AECh. 11 - Prob. 11F.3BECh. 11 - Prob. 11F.4AECh. 11 - Prob. 11F.4BECh. 11 - Prob. 11F.5AECh. 11 - Prob. 11F.5BECh. 11 - Prob. 11F.6AECh. 11 - Prob. 11F.6BECh. 11 - Prob. 11F.7AECh. 11 - Prob. 11F.7BECh. 11 - Prob. 11F.8AECh. 11 - Prob. 11F.8BECh. 11 - Prob. 11F.9AECh. 11 - Prob. 11F.9BECh. 11 - Prob. 11F.10AECh. 11 - Prob. 11F.10BECh. 11 - Prob. 11F.11AECh. 11 - Prob. 11F.11BECh. 11 - Prob. 11F.12AECh. 11 - Prob. 11F.12BECh. 11 - Prob. 11F.13AECh. 11 - Prob. 11F.13BECh. 11 - Prob. 11F.1PCh. 11 - Prob. 11F.2PCh. 11 - Prob. 11F.3PCh. 11 - Prob. 11F.4PCh. 11 - Prob. 11F.5PCh. 11 - Prob. 11F.6PCh. 11 - Prob. 11F.7PCh. 11 - Prob. 11F.8PCh. 11 - Prob. 11F.9PCh. 11 - Prob. 11F.10PCh. 11 - Prob. 11F.11PCh. 11 - Prob. 11F.12PCh. 11 - Prob. 11G.1DQCh. 11 - Prob. 11G.2DQCh. 11 - Prob. 11G.3DQCh. 11 - Prob. 11G.4DQCh. 11 - Prob. 11G.5DQCh. 11 - Prob. 11G.1AECh. 11 - Prob. 11G.1BECh. 11 - Prob. 11G.2AECh. 11 - Prob. 11G.2BECh. 11 - Prob. 11G.1PCh. 11 - Prob. 11G.2PCh. 11 - Prob. 11G.3PCh. 11 - Prob. 11G.4PCh. 11 - Prob. 11G.5PCh. 11 - Prob. 11G.6PCh. 11 - Prob. 11.1IACh. 11 - Prob. 11.5IACh. 11 - Prob. 11.8IA
Knowledge Booster
Background pattern image
Chemistry
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, chemistry and related others by exploring similar questions and additional content below.
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