
Concept explainers
(i)
Interpretation:
The ratio A/B for transitions with 70.8 pm 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
AB=8πhv3c3
(i)

Answer to Problem 11A.1AE
The ratio of A/B for transitions with 70.8 pm X-rays is 0.0468 J⋅s m−3_.
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 70.8 pm.
The conversion of pm into m is done as shown below.
1 pm=10−12 m
Therefore, the conversion of 70.8 pm into m is as follows.
1 pm=10−12 m70.8 pm=70.8×10−12 m
Substitute the value of λ in the equation (3).
AB=8πhλ3=8×3.14×(6.625×10−34 Js)(70.8×10−12 m)3=0.0468 J⋅s m−3_
Therefore, the ratio of A/B for transitions with 70.8 pm X-rays is 0.0468 J⋅s m−3_.
(ii)
Interpretation:
The ratio A/B for transitions with 500 nm 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)

Answer to Problem 11A.1AE
The ratio A/B for transitions with 500 nm visible light is 1.33×10−13 J⋅s m−3_.
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 500 nm.
The conversion of nm into m is done as shown below.
1 nm=10−9 m
Therefore, the conversion of 500 nm into m is as follows.
1 nm=10−9 m500 nm=500×10−9 m
Substitute the value of λ in the equation (3).
AB=8πhλ3=8×3.14×(6.625×10−34 Js)(500×10−9 m)3=1.33×10−13 J⋅s m−3_
Therefore, the ratio A/B for transitions with 500 nm visible light is 1.33×10−13 J⋅s m−3_.
(iii)
Interpretation:
The ratio A/B for transitions with 3000 cm−1 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)

Answer to Problem 11A.1AE
The ratio A/B for transitions with 3000 cm−1 infrared radiation is 4.5×10−28 J⋅s m−3_.
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.
ˉv=1λ
The above equation can be written as shown below.
λ=1ˉv (4)
Substitute the value of λ in the equation (4).
AB=8πhˉv3 (5)
The given value of wave number is 3000 cm−1.
The conversion of cm into m is done as shown below.
1 cm=10−2 m
Therefore, the conversion of 3000 cm−1 into m is done as shown below.
1 cm=10−2 m3000 cm=3000×10−2 m
Substitute the value of wave number in the equation (5).
AB=8πhˉv3=8×3.14×(6.625×10−34 J⋅s)×(3000×10−2 m)3=4493.3×10−28 J⋅s m−3≃4.5×10−28 J⋅s m−3_
Therefore, the ratio A/B for transitions with 3000 cm−1 infrared radiation is 4.5×10−28 J⋅s m−3_.
Want to see more full solutions like this?
Chapter 11 Solutions
Atkins' Physical Chemistry
- Curved arrows are used to illustrate the flow of electrons. Using the provided starting and product structures, draw the curved electron-pushing arrows for the following reaction or mechanistic step(s). Be sure to account for all bond-breaking and bond-making steps. Problem 164 of N Select to Add Arrows CHI CH 1 1 1 Parrow_forwardusing these can you help me , I guess convert them to lewis dit structures or full drawn out skeletal and I guess is that what would help me depict the bond angle.arrow_forwardShow reaction mechanism with explanation.don't give Ai generated solutionarrow_forward
- Please answer the questions and provide detailed explanations.arrow_forwardShow reaction mechanism. Don't give Ai generated solutionarrow_forwardPlease answer the questions and provide detailed explanation. Please also include the Hydrogens that are on the molecule to show how many signals there are.arrow_forward
- Capp aktiv.com Part of Speech Table for Assi x Aktiv Learning App K Curved arrows are used to illustrate the flow of electrons. Using the provided starting and product structures, draw the curved electron-pushing arrows for the following reaction or mechanistic step(s). Be sure to account for all bond-breaking and bond-making steps. Problem 232 of 10 10: Mg Select to Add Arrows Br O H :0 CI:O H Mg THE + dy Undo Reset Done Brarrow_forwardPlease answer the question and provide a detailed drawing of the structure. If there will not be a new C – C bond, then the box under the drawing area will be checked. Will the following reaction make a molecule with a new C – C bond as its major product: Draw the major organic product or products, if the reaction will work. Be sure you use wedge and dash bonds if necessary, for example to distinguish between major products with different stereochemistry.arrow_forwardNeed help with witharrow_forward
- Please answer the questions and provide detailed explanations.arrow_forwardsolve pleasearrow_forwardPlease answer the question and provide a detailed drawing of the structure. If there will not be a new C – C bond, then the box under the drawing area will be checked. Will the following reaction make a molecule with a new C – C bond as its major product: Draw the major organic product or products, if the reaction will work. Be sure you use wedge and dash bonds if necessary, for example to distinguish between major products with different stereochemistry.arrow_forward
- ChemistryChemistryISBN:9781305957404Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCostePublisher:Cengage LearningChemistryChemistryISBN:9781259911156Author:Raymond Chang Dr., Jason Overby ProfessorPublisher:McGraw-Hill EducationPrinciples of Instrumental AnalysisChemistryISBN:9781305577213Author:Douglas A. Skoog, F. James Holler, Stanley R. CrouchPublisher:Cengage Learning
- Organic ChemistryChemistryISBN:9780078021558Author:Janice Gorzynski Smith Dr.Publisher:McGraw-Hill EducationChemistry: Principles and ReactionsChemistryISBN:9781305079373Author:William L. Masterton, Cecile N. HurleyPublisher:Cengage LearningElementary Principles of Chemical Processes, Bind...ChemistryISBN:9781118431221Author:Richard M. Felder, Ronald W. Rousseau, Lisa G. BullardPublisher:WILEY





