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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- You know that the wavenumbers of the rotational transition J = 1← 0 for 1H35Cl and2H35Cl are 20.8784 and 10.7840cm-1, respectively. Accurate atomic masses are1.007825 and 2.0140 for 1H and 2H, respectively. The mass of 35Cl is34.96885. Conclude based on this information that the bond lengths are the sameor differentarrow_forwardThe nuclear spin of deuterium, D, is I= 1. Calculatethe ratio of the number of ways of achieving rotational statesw ith odd and even values of J.arrow_forwardwhich of the following is a reason electronic spectra of molecules typically contain broad peaks? a. all transtions are allowed, b. excited states have finite lifetimes, c. the molecules are stationary, d. all transitions are forbiddenarrow_forward
- A scientist investigates the possibility of neutron spin resonance, and has available a commercial NMR spectrometer operating at 300 MHz for 1H nuclei. What is the NMR frequency of the neutron in this spectrometer? What is the relative population difference at room temperature? Which is the lower energy spin state of the neutron?arrow_forwardGround state sodium has a term symbol of 2S1/2. What are the possible term symbols for the product of an allowed transition for ground state sodium?arrow_forwardThe following parameters describe the electronic ground state and an excited electronic state of SnO: ᷉ B = 0.3540 cm−1, ᷉ B' = 0.3101 cm−1. Which branch of the transition between them shows a head? At what value of J will it occur?arrow_forward
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