Concept explainers
(a)
Interpretation:
The given integrals of the wavefunctions of particles-in-boxes are to be evaluated by using equation 10.28.
Concept introduction:
For the orthogonality of the two different wave functions, the product of the wave functions is integrated over the entire limits. It is expressed by the equation as given below.
Where,
Answer to Problem 10.88E
The value of given integral of wavefunction is
Explanation of Solution
The combined expression for orthogonality and normality of wave functions is given by the equation 10.28 as shown below.
Where,
•
The given integrals of the wavefunctions is
Therefore, the value of given integral of wavefunction is
The value of given integral of wavefunction is
(b)
Interpretation:
The given integrals of the wavefunctions of particles-in-boxes are to be evaluated by using equation 10.28.
Concept introduction:
For the orthogonality of the two different wave functions, the product of the wave functions is integrated over the entire limits. It is expressed by the equation as given below.
Where,
Answer to Problem 10.88E
The value of given integral of wavefunction is
Explanation of Solution
The combined expression for orthogonality and normality of wave functions is given by the equation 10.28 as shown below.
Where,
•
The given integrals of the wavefunctions is
Therefore, the value of given integral of wavefunction is
The value of given integral of wavefunction is
(c)
Interpretation:
The given integrals of the wavefunctions of particles-in-boxes are to be evaluated by using equation 10.28.
Concept introduction:
The Schrödinger equation is used to find the allowed energy levels for electronic transitions in the
Where,
•
•
•
Answer to Problem 10.88E
The value of given integral of wavefunction is
Explanation of Solution
The combined expression for orthogonality and normality of wave functions is given by the equation 10.28 as shown below.
Where,
•
The given integrals of the wavefunctions is
Thus, the given wave function can be expressed as follows:
Hence, the given wave function is expressed as
The value of given wave function is calculated as follows:
Substitute the value of
Therefore, the value of given integral of wavefunction is
The value of given integral of wavefunction is
(d)
Interpretation:
The given integrals of the wavefunctions of particles-in-boxes are to be evaluated by using equation 10.28.
Concept introduction:
The Schrödinger equation is used to find the allowed energy levels for electronic transitions in the quantum mechanics. It is generally expressed as follows.
Where,
•
•
•
Answer to Problem 10.88E
The value of given integral of wavefunction is
Explanation of Solution
The combined expression for orthogonality and normality of wave functions is given by the equation 10.28 as shown below.
Where,
•
The given integrals of the wavefunctions is
Thus, the given wave function can be expressed as follows:
Hence, the given wave function is expressed as
The value of given wave function is calculated as follows:
Therefore, the value of given integral of wavefunction is
The value of given integral of wavefunction is
(e)
Interpretation:
The given integrals of the wavefunctions of particles-in-boxes are to be evaluated by using equation 10.28.
Concept introduction:
For the orthogonality of the two different wave functions, the product of the wave functions is integrated over the entire limits. It is expressed by the equation as given below.
Where,
Answer to Problem 10.88E
The value of given integral of wavefunction is
Explanation of Solution
The combined expression for orthogonality and normality of wave functions is given by the equation 10.28 as shown below.
Where,
•
The given integrals of the wavefunctions is
Therefore, the value of given integral of wavefunction is
The value of given integral of wavefunction is
(f)
Interpretation:
The given integrals of the wavefunctions of particles-in-boxes are to be evaluated by using equation 10.28.
Concept introduction:
For the orthogonality of the two different wave functions, the product of the wave functions is integrated over the entire limits. It is expressed by the equation as given below.
Where,
Answer to Problem 10.88E
The value of given integral of wavefunction is
Explanation of Solution
The combined expression for orthogonality and normality of wave functions is given by the equation 10.28 as shown below.
Where,
•
The given integrals of the wavefunctions is
Therefore, the value of given integral of wavefunction is
The value of given integral of wavefunction is
(g)
Interpretation:
The given integrals of the wavefunctions of particles-in-boxes are to be evaluated by using equation 10.28.
Concept introduction:
The Schrödinger equation is used to find the allowed energy levels for electronic transitions in the quantum mechanics. It is generally expressed as follows.
Where,
•
•
•
Answer to Problem 10.88E
The value of given integral of wavefunction is
Explanation of Solution
The combined expression for orthogonality and normality of wave functions is given by the equation 10.28 as shown below.
Where,
•
The given integral of the wavefunctions is
Thus, the given wave function can be expressed as follows:
Hence, the given wave function is expressed as
The value of given wave function is calculated as follows:
Substitute the value of
Therefore, the value of given integral of wavefunction is
The value of given integral of wavefunction is
(h)
Interpretation:
The given integrals of the wavefunctions of particles-in-boxes are to be evaluated by using equation 10.28.
Concept introduction:
The Schrödinger equation is used to find the allowed energy levels for electronic transitions in the quantum mechanics. It is generally expressed as follows.
Where,
•
•
•
Answer to Problem 10.88E
The value of given integral of wavefunction is
Explanation of Solution
The combined expression for orthogonality and normality of wave functions is given by the equation 10.28 as shown below.
Where,
•
The given integrals of the wavefunctions is
Thus, the given wave function can be expressed as follows:
Hence, the given wave function is expressed as
The value of given wave function is calculated as follows:
Therefore, the value of given integral of wavefunction is
The value of given integral of wavefunction is
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Chapter 10 Solutions
Physical Chemistry
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