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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