Physical Chemistry
Physical Chemistry
2nd Edition
ISBN: 9781133958437
Author: Ball, David W. (david Warren), BAER, Tomas
Publisher: Wadsworth Cengage Learning,
bartleby

Concept explainers

bartleby

Videos

Question
Book Icon
Chapter 16, Problem 16.15E
Interpretation Introduction

Interpretation:

The ΔE values experienced by the ground state (4F3/2) energy levels of V atom are to be calculated.

Concept Introduction:

The change in energy (ΔE) of the state depends on the strength of the magnetic field (B) and the z-component quantum number (ML) in the presence of magnetic field. The expression for the change in energy (ΔE) is written below.

ΔE=μBMLB

The value of (ML) can be positive, negative or zero. Hence, the change in energy (ΔE) can be positive, negative or zero. The change in energy (ΔE) of the state is equal to the amount of splitting.

Expert Solution & Answer
Check Mark

Answer to Problem 16.15E

The ΔE values experienced by the ground state (4F3/2) energy levels of V atom are 3.10×1024J, 1.03×1024J, +1.03×1024J and +3.10×1024J.

Explanation of Solution

The ΔE values experienced by the ground state (4F3/2) energy levels of V atom are calculated by the formula given below.

ΔE=gμBMJB…(1)

Where,

μB is Bohr magneto (9.274×1024J/T).

(MJ) is the z-component quantum number.

g is Lande g factor.

B is earth’s magnetic field.

The value of g is calculated by the formula given below.

g=1+j(j+1)+s(s+1)l(l+1)2j(j+1)…(2)

Where,

j, s and l are quantum numbers.

The values of j, s and l for (4F3/2) state are 3/2, 3/2 and 3.

Substitute the values of j, s and l in equation (2).

g=1+3/2(3/2+1)+3/2(3/2+1)3(3+1)2×3/2(3/2+1)=1+15/4+15/41230/4=1+30/41230/4=118/430/4

Simplify the above equation.

g=135=25

One gauss equals to 1.0×104T. Therefore 5.57×103G will be equal to 0.557T.

The value of μB and B are (9.274×1024J/T) and 0.557T.

Substitute the values of μB, B and g in equation (1).

When MJ=(32),

ΔE=gμBMJB=25×9.274×1024J/T×(32)×0.557T=(35)×5.165×1024J=3.10×1024J

When MJ=(12),

ΔE=gμBMJB=25×9.274×1024J/T×(12)×0.557T=(15)×5.165×1024J=1.03×1024J

When MJ=0, ΔE will be zero.

When MJ=32,

ΔE=gμBMJB=25×9.274×1024J/T×32×0.557T=35×5.165×1024J=3.10×1024J

When MJ=12,

ΔE=gμBMJB=25×9.274×1024J/T×12×0.557T=15×5.165×1024J=1.03×1024J

Conclusion

The ΔE values experienced by the ground state (4F3/2) energy levels of V atom are 3.10×1024J, 1.03×1024J, +1.03×1024J and +3.10×1024J.

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
What is ΔE for the transition of an electron from n = 7 to n = 3 in a hydrogen atom? What is the frequency, ν,  of the spectral line produced?
It is known that the possible values for the magnetic quantum number mι are -5, -4, -3, -2, -1, 0, +1, +2, +3, +4 and +5. What is (a) the orbital quantum number ι and (b) the smallest possible value of the principal quantum number n?
(a) Calculate the energy (in joules) for ground state electron in Li2+. Report your answer to 4 significant figures. (b) What is the wave length of the light, in nanometers, required to raise anelectron in the Li2+ ion from n =1 to n = 4 level
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.
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
  • Text book image
    General Chemistry - Standalone book (MindTap Cour...
    Chemistry
    ISBN:9781305580343
    Author:Steven D. Gammon, Ebbing, Darrell Ebbing, Steven D., Darrell; Gammon, Darrell Ebbing; Steven D. Gammon, Darrell D.; Gammon, Ebbing; Steven D. Gammon; Darrell
    Publisher:Cengage Learning
    Text book image
    Chemistry: Principles and Practice
    Chemistry
    ISBN:9780534420123
    Author:Daniel L. Reger, Scott R. Goode, David W. Ball, Edward Mercer
    Publisher:Cengage Learning
    Text book image
    Chemistry: The Molecular Science
    Chemistry
    ISBN:9781285199047
    Author:John W. Moore, Conrad L. Stanitski
    Publisher:Cengage Learning
  • Text book image
    Chemistry
    Chemistry
    ISBN:9781305957404
    Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
    Publisher:Cengage Learning
    Text book image
    Chemistry: An Atoms First Approach
    Chemistry
    ISBN:9781305079243
    Author:Steven S. Zumdahl, Susan A. Zumdahl
    Publisher:Cengage Learning
    Text book image
    Chemistry
    Chemistry
    ISBN:9781133611097
    Author:Steven S. Zumdahl
    Publisher:Cengage Learning
Text book image
General Chemistry - Standalone book (MindTap Cour...
Chemistry
ISBN:9781305580343
Author:Steven D. Gammon, Ebbing, Darrell Ebbing, Steven D., Darrell; Gammon, Darrell Ebbing; Steven D. Gammon, Darrell D.; Gammon, Ebbing; Steven D. Gammon; Darrell
Publisher:Cengage Learning
Text book image
Chemistry: Principles and Practice
Chemistry
ISBN:9780534420123
Author:Daniel L. Reger, Scott R. Goode, David W. Ball, Edward Mercer
Publisher:Cengage Learning
Text book image
Chemistry: The Molecular Science
Chemistry
ISBN:9781285199047
Author:John W. Moore, Conrad L. Stanitski
Publisher:Cengage Learning
Text book image
Chemistry
Chemistry
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Cengage Learning
Text book image
Chemistry: An Atoms First Approach
Chemistry
ISBN:9781305079243
Author:Steven S. Zumdahl, Susan A. Zumdahl
Publisher:Cengage Learning
Text book image
Chemistry
Chemistry
ISBN:9781133611097
Author:Steven S. Zumdahl
Publisher:Cengage Learning
The Bohr Model of the atom and Atomic Emission Spectra: Atomic Structure tutorial | Crash Chemistry; Author: Crash Chemistry Academy;https://www.youtube.com/watch?v=apuWi_Fbtys;License: Standard YouTube License, CC-BY