Concept explainers
(a)
Interpretation:
The complex conjugate of the wave function
Concept introduction:
For the normalization of the wave function, the wave function is integrated as a product of its conjugate over the entire limits. It is expressed by the equation as given below.
Where,
•
•
•
(b)
Interpretation:
The complex conjugate of the wave function
Concept introduction:
For the normalization of the wave function, the wave function is integrated as a product of its conjugate over the entire limits. It is expressed by the equation as given below.
Where,
•
•
•
(c)
Interpretation:
The complex conjugate of the wave function
Concept introduction:
For the normalization of the wave function, the wave function is integrated as a product of its conjugate over the entire limits. It is expressed by the equation as given below.
Where,
•
•
•
(d)
Interpretation:
The complex conjugate of the wave function
Concept introduction:
For the normalization of the wave function, the wave function is integrated as a product of its conjugate over the entire limits. It is expressed by the equation as given below.
Where,
•
•
•
(e)
Interpretation:
The complex conjugate of the wave function
Concept introduction:
For the normalization of the wave function, the wave function is integrated as a product of its conjugate over the entire limits. It is expressed by the equation as given below.
Where,
•
•
•
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Chapter 10 Solutions
Physical Chemistry
- A 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_forwardAssume that the states of the π electrons of a conjugated molecule can be approximated by the wavefunctions of a particle in a one-dimensional box, and that the magnitude of the dipole moment can be related to the displacement along this length by μ = −ex. Show that the transition probability for the transition n = 1 → n = 2 is non-zero, whereas that for n = 1 → n = 3 is zero. Hints: The following relation will be useful: sin x sin y = 1/2cos(x − y) − 1/2cos(x + y). Relevant integrals are given in the Resource section.arrow_forwardFor the same system as in Exercise E7C.3(a) (Functions of the form sin(nπx/L), where n = 1, 2, 3 …, are wavefunctions in a region of length L (between x = 0 and x = L). Show that the wavefunctions with n = 1 and 2 are orthogonal; you will find the necessary integrals in the Resource section) ,show that the wavefunctions with n = 2 and 4 are orthogonal.arrow_forward
- Determine the energetic difference between state n = 2 and n = 1 for a proton in a one-dimensional box of length 100 nm. At what wavelength does that energy correspond?arrow_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_forwardFor a particle in a box of length L and in the state with n = 3, at what positions is the probability density a maximum? At what positions is the probability density zero?arrow_forward
- Which of the following transitions are allowed in the electronic emission spectrum of a hydrogenic atom: (i) 2s → 1s, (ii) 2p → 1s, (iii) 3d → 2p?arrow_forwardFor the system described in Exercise E7B.1(a) (A possible wavefunction for an electron in a region of length L (i.e. from x = 0 to x = L) is sin(2πx/L). Normalize this wavefunction (to 1)), what is the probability of finding the electron in the range dx at x = L/2?arrow_forwardNormalize the wave function ψ= A sin (nπ/a x) by finding the value of the constant A when the particle is restricted to move in one dimensional box of width ‘a’.arrow_forward
- By considering the integral ∫02π ψ*ml ψml dϕ, where ml≠m'l, confirm that wavefunctions for a particle in a ring with different values of the quantum number ml are mutually orthogonal.arrow_forwardWhich of the following functions can be normalized (in all cases the range for x is from x = −∞ to ∞, and a is a positive constant): (i) sin(ax);(ii) cos(ax) e-x^2? Which of these functions are acceptable as wavefunctions?arrow_forwardWhich of the following functions can be normalized (in all cases the range for x is from x= (-infinity) to (infinity), and a is a positive constant): (i) sin(ax); (ii) cos(ax)e-x^2? Which of these functions are acceptable as wavefunctions? Source: Atkins Physical Chemistry 11th Edition, E7B.4(b)arrow_forward
- Introductory Chemistry: A FoundationChemistryISBN:9781337399425Author:Steven S. Zumdahl, Donald J. DeCostePublisher:Cengage Learning