Concept explainers
For a particle in a state having the wavefunction
(a)
(c)
(e)
Plot the probabilities versus
(a)
Interpretation:
The probability for the particle having wavefunction
Concept introduction:
For the normalization of the wavefunction, the wavefunction is integrated as a product of its conjugate over the entire limits. It is expressed by the equation as given below.
Where,
•
•
•
Answer to Problem 10.26E
The probability for the particle having wavefunction
Explanation of Solution
For the probability of the wavefunction the expression is as follows.
Where,
•
•
•
•
Substitute the values in the above equation as follows.
The above expression is simplified as follows.
The probability for the particle having wavefunction
(b)
Interpretation:
The probability for the particle having wavefunction
Concept introduction:
For the normalization of the wavefunction, the wavefunction is integrated as a product of its conjugate over the entire limits. It is expressed by the equation as given below.
Where,
•
•
•
Answer to Problem 10.26E
The probability for the particle having wavefunction
Explanation of Solution
For the probability of the wavefunction the expression is as follows.
Where,
•
•
•
•
Substitute the values in the above equation as follows.
The above expression is simplified as follows.
The probability for the particle having wavefunction
(c)
Interpretation:
The probability for the particle having wavefunction
Concept introduction:
For the normalization of the wavefunction, the wavefunction is integrated as a product of its conjugate over the entire limits. It is expressed by the equation as given below.
Where,
•
•
•
Answer to Problem 10.26E
The probability for the particle having wavefunction
Explanation of Solution
For the probability of the wavefunction the expression is as follows.
Where,
•
•
•
•
Substitute the values in the above equation as follows.
The above expression is simplified as follows.
The probability for the particle having wavefunction
(d)
Interpretation:
The probability for the particle having wavefunction
Concept introduction:
For the normalization of the wavefunction, the wavefunction is integrated as a product of its conjugate over the entire limits. It is expressed by the equation as given below.
Where,
•
•
•
Answer to Problem 10.26E
The probability for the particle having wavefunction
Explanation of Solution
For the probability of the wavefunction the expression is as follows.
Where,
•
•
•
•
Substitute the values in the above equation as follows.
The above expression is simplified as follows.
The probability for the particle having wavefunction
(e)
Interpretation:
The probability for the particle having wavefunction
Concept introduction:
For the normalization of the wavefunction, the wavefunction is integrated as a product of its conjugate over the entire limits. It is expressed by the equation as given below.
Where,
•
•
•
Answer to Problem 10.26E
The probability for the particle having wavefunction
Explanation of Solution
For the probability of the wavefunction the expression is as follows.
Where,
•
•
•
•
Substitute the values in the above equation as follows.
The above expression is simplified as follows.
Theplot the probabilities versus
Figure 1
The plot shows the probability for the given wave function. According to this plot, the probability of finding the particle is maximum in the range of
The probability for the particle having wavefunction
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Chapter 10 Solutions
Physical Chemistry
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- Introductory Chemistry: A FoundationChemistryISBN:9781337399425Author:Steven S. Zumdahl, Donald J. DeCostePublisher:Cengage Learning