Concept explainers
(a)
Interpretation:
The Lande
Concept introduction:
The change in energy
The value of
(b)
Interpretation:
The reason why need never worry about this unusual value is to be stated.
Concept introduction:
The change in energy
The value of
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Chapter 16 Solutions
Physical Chemistry
- Consider an Ar atom trapped in square box with length 1 m. Assume that the energy of the Ar atom is equal to thermal energy: 3kBT/2 at 25 degrees Celsius. a)Use the model of a particle in a box and assume the particle is at the state: n = nx = ny = nz , calculate n of the above system. b) What is the energy separation between the states (n, n, n) and (n + 1, n, n). c) Assume that all the energy of the particle is from kinetic energy. Calculate the de Broglie wavelength of the particle. d) Based on your answers above, would you treat this particle classically or quantumly? Explain your answer.arrow_forwardCalculate the momentum of an X-ray photon with a wavelength of 0.17nm. How does this value compare with the momentum of a free electron that has been accelerated through a potential difference of 5000 volts? (Hint: electron mass, m, = 9.10938 x 10" kg; electron charge e = 1.602 x 10"C; speed of light e = 3.0 x 10* m.s'; 1.00 J= 1.00 VC; h = 6.626 x 10"J.s. The various energy units are: 1 J= 1 kg.m°s³, 1.00 eV =1VC, leV= 1.602 x 10"J, 1J= 6.242 x 10" eV, etc.). %3Darrow_forwardCalculate the momentum of an X-ray photon with a wavelength of 0.17nm. How does this value compare with the momentum of a free electron that has been accelerated through a potential difference of 5000 volts? (Hint: electron mass, m, = 9.10938 x 10" kg; electron charge e = 1.602 x 10"C; speed of light e = 3.0 x 10° m.s'; 1.00 J= 1.00 VC; h = 6.626 x 10"J.s. The various energy units are: 1 J=1 kg.m's", 1.00 cV =1VC, leV = 1.602 x 10"J, 1J=6.242 x 10" eV, etc.). %3D %3Darrow_forward
- Consider a fictitious one-dimensional system with one electron.The wave function for the electron, drawn below, isψ (x)= sin x from x = 0 to x = 2π. (a) Sketch the probabilitydensity, ψ2(x), from x = 0 to x = 2π. (b) At what value orvalues of x will there be the greatest probability of finding theelectron? (c) What is the probability that the electron willbe found at x = π? What is such a point in a wave functioncalled?arrow_forwardConsider a particle of mass m confined to a one-dimensional box of length L and in a state with normalized wavefunction ψn. (a) Without evaluating any integrals, explain why ⟨x⟩ = L/2. (b) Without evaluating any integrals, explain why ⟨px⟩ = 0. (c) Derive an expression for ⟨x2⟩ (the necessary integrals will be found in the Resource section). (d) For a particle in a box the energy is given by En = n2h2/8mL2 and, because the potential energy is zero, all of this energy is kinetic. Use this observation and, without evaluating any integrals, explain why <p2x> = n2h2/4L2.arrow_forwardThe energy equation for a particle in a cubic box of dimensions Lx = L, = Lz is Eux, w. = 8 mL? For a particle in a cubic box, how many degenerate energy levels have energy equal to 14 h/8 mL? 1 12 8. 3arrow_forward
- Use the References to access important values if needed for this question. Complete the following table for the function y = -6z + 26. 1 2 3 Submitarrow_forward(a) For a particle in the stationary state n of a one dimensional box of length a, find the probability that the particle is in the region 0 x a/4. (b) Calculate this probability for n = 1, 2, and 3 Sketch and | |2 for the n = 4 and n = 5 states of a particle in a one-dimensional box.arrow_forwardBohr’s model can be used for hydrogen-like ions—ions thathave only one electron, such as He + and Li2+ . (a) Why isthe Bohr model applicable to He + ions but not to neutral Heatoms? (b) The ground-state energies of H, He + , and Li2 + aretabulated as follows: By examining these numbers, propose a relationship betweenthe ground-state energy of hydrogen-like systems and thenuclear charge, Z. (c) Use the relationship you derive in part(b) to predict the ground-state energy of the C5+ ion.arrow_forward
- (a) What is the lowest possible value of the principal quantum number (n) when the angular momentum quantum number (ℓ) is 1? (b) What are the possible values of the angular momentum quantum number (ℓ) when the principal quantum number (n) is 4 and the magnetic quantum number (mℓ) is 0?arrow_forwardFor a particle in a cubic box of length a, give the degree of degeneracy of the energy level with energy (a) 21h2/8ma2; (b) 24h2/8ma2arrow_forward106. Combining two real wave functions ₁ and 2, the following functions are constructed: A = ₁ + $₂₂ B = = ₁ +i0₂, C = ₁ −i0₂, D=i(0₁ +0₂). The correct statement will then be (a) A and B represent the same state (c) A and D represents the same state (b) A and C represent the same state. (d) B and D represent the same state.arrow_forward
- Physical ChemistryChemistryISBN:9781133958437Author:Ball, David W. (david Warren), BAER, TomasPublisher:Wadsworth Cengage Learning,Introductory Chemistry: A FoundationChemistryISBN:9781337399425Author:Steven S. Zumdahl, Donald J. DeCostePublisher:Cengage LearningChemistry: Matter and ChangeChemistryISBN:9780078746376Author:Dinah Zike, Laurel Dingrando, Nicholas Hainen, Cheryl WistromPublisher:Glencoe/McGraw-Hill School Pub Co