Concept explainers
What are the values of
(a)
Interpretation:
The values of
Concept introduction:
In quantum mechanics, the wavefunction is given by
Answer to Problem 11.73E
The value of
Explanation of Solution
The energy for the given wave function is given by the formula,
Where,
•
•
•
•
The total angular momentum is calculated by the formula,
Where,
•
The
Where,
•
The given wavefunctions for electron of
Substitute the value of
Thus, the value of
Substitute the value of
Thus, the value of
Substitute the value of
Thus, the value of
Hence, the value of
The value of
(b)
Interpretation:
The values of
Concept introduction:
In quantum mechanics, the wavefunction is given by
Answer to Problem 11.73E
The value of
Explanation of Solution
The energy for the given wave function is given by the formula,
Where,
•
•
•
•
The total angular momentum is calculated by the formula,
Where,
•
The
Where,
•
The given wavefunctions for electron of
Substitute the value of
Thus, the value of
Substitute the value of
Thus, the value of
Substitute the value of
Thus, the value of
Hence, the value of
The value of
(c)
Interpretation:
The values of
Concept introduction:
In quantum mechanics, the wavefunction is given by
Answer to Problem 11.73E
The value of
Explanation of Solution
The energy for the given wave function is given by the formula,
Where,
•
•
•
•
The total angular momentum is calculated by the formula,
Where,
•
The
Where,
•
The given wavefunctions for electron of
Substitute the value of
Thus, the value of
Substitute the value of
Thus, the value of
Substitute the value of
Thus, the value of
Hence, the value of
The value of
(d)
Interpretation:
The values of
Concept introduction:
In quantum mechanics, the wavefunction is given by
Answer to Problem 11.73E
The value of
Explanation of Solution
The energy for the given wave function is given by the formula,
Where,
•
•
•
•
The total angular momentum is calculated by the formula,
Where,
•
The
Where,
•
The given wavefunctions for electron of
Substitute the value of
Thus, the value of
Substitute the value of
Thus, the value of
Substitute the value of
Thus, the value of
Hence, the value of
The value of
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Chapter 11 Solutions
Physical Chemistry
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- (a) What are the possible values for mℓ when the principal quantum number (n) is 2 and the angular momentum quantum number (ℓ) is 0? (b) What are the possible values for mℓ when the principal quantum number (n) is 3 and the angular momentum quantum number (ℓ) is 2?arrow_forwardi need the answer quicklyarrow_forwardA normalized wavefunction for a particle confined between 0 and L in the x direction is ψ = (2/L)1/2 sin(πx/L). Suppose that L = 10.0 nm. Calculate the probability that the particle is (a) between x = 4.95 nm and 5.05 nm, (b) between x = 1.95 nm and 2.05 nm, (c) between x = 9.90 nm and 10.00 nm, (d) between x = 5.00 nm and 10.00 nm.arrow_forward
- last three subpartsarrow_forwardThe ground-state wavefunction for a particle confined to a one dimensional box of length L is Ψ =(2/L)½ sin (πx/L) Suppose the box 10.0 nm long. Calculate the probability that the particle is: (a) between x = 4.95 nm and 5.05 nm (b) between 1.95 nm and 2.05 nm, (c) between x = 9.90 and 10.00 nm, (d) in the right half of the box and (e) in the central third of the box.arrow_forward5. Determine yy for each of the following wavefunctions: (i =V-1) a) y (x) = e b) y(0) = sin 0 +i cose c) w(x) = A · e*.arrow_forward
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