Concept explainers
(a)
Interpretation:
The value of
Concept introduction:
Different linearly independent wavefunctions that have same energy are called degenerate. This is expressed in terms of degeneracy. If two functions are having same energy then they are called doubly degenerate and so on. The degeneracy for nuclear state is given as,
Where,
•
Answer to Problem 18.1E
The value of
Explanation of Solution
From Appendix
The nuclear spin of
The degeneracy for nuclear state is given as,
Where,
•
Substitute the value of
The partition function for nucleus is given as,
Substitute the value of
Therefore, the value of
The value of
(b)
Interpretation:
The value of
Concept introduction:
Different linearly independent wavefunctions that have same energy are called degenerate. This is expressed in terms of degeneracy. If two functions are having same energy then they are called doubly degenerate and so on. The degeneracy for nuclear state is given as,
Where,
•
Answer to Problem 18.1E
The value of
Explanation of Solution
From Appendix
The nuclear spin of
The degeneracy for nuclear state is given as,
Where,
•
Substitute the value of
The partition function for nucleus is given as,
Substitute the value of
Therefore, the value of
The value of
(c)
Interpretation:
The value of
Concept introduction:
Different linearly independent wavefunctions that have same energy are called degenerate. This is expressed in terms of degeneracy. If two functions are having same energy then they are called doubly degenerate and so on. The degeneracy for nuclear state is given as,
Where,
•
Answer to Problem 18.1E
The value of
Explanation of Solution
From Appendix
The nuclear spin of
The degeneracy for nuclear state is given as,
Where,
•
Substitute the value of
The partition function for nucleus is given as,
Substitute the value of
Therefore, the value of
Hydrogen is the only atom that has no neutrons in its nucleus. Therefore, the nuclear degeneracy of
The value of
(d)
Interpretation:
The value of
Concept introduction:
Different linearly independent wavefunctions that have same energy are called degenerate. This is expressed in terms of degeneracy. If two functions are having same energy then they are called doubly degenerate and so on. The degeneracy for nuclear state is given as,
Where,
•
Answer to Problem 18.1E
The value of
Explanation of Solution
From Appendix
The nuclear spin of
The degeneracy for nuclear state is given as,
Where,
•
Substitute the value of
The partition function for nucleus is given as,
Substitute the value of
Therefore, the value of
A deuterium atom contains one proton and one neutron. The spin of proton and neutron does not cancel each other but combines with each other. Therefore, the nuclear degeneracy of deuterium atom is due to the presence of a proton and a neutron.
The value of
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Chapter 18 Solutions
Physical Chemistry
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- If a sample is placed in a magnetic field of applied field strength = 1.1 Tesla, the spin-up and spin-down 1H nuclei show an energy difference that corresponds to a photon with frequency = 60 MHz. If this same sample is moved into the vicinity of a magnetic field of strength = 5.5 Tesla, what will be the frequency of a photon that could match the energy difference of the spin-up and spin-down states?arrow_forwardThe requirement for high spin is that_ а. Ao > P, where P is the pairing energy b. Ao = 2P С. Ao = P d. Ao < Parrow_forwardThe electronic configuration of iron, 26 Fe, is 1s²2s22p63s²3p63d64s². There are 6 electrons in the outermost, partially-filled sub-shell 3d. . What are the allowed values of the total spin S for iron? . What are the possible values of the total orbital angular momentum L when the spin multiplicity is maximized?arrow_forward
- Physical ChemistryChemistryISBN:9781133958437Author:Ball, David W. (david Warren), BAER, TomasPublisher:Wadsworth Cengage Learning,