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- For a particle in a state having the wavefunction =2asinxa in the range x=0toa, what is the probability that the particle exists in the following intervals? a x=0to0.02ab x=0.24ato0.26a c x=0.49ato0.51ad x=0.74ato0.76a e x=0.98ato1.00a Plot the probabilities versus x. What does your plot illustrate about the probability?What is the degeneracy of an h subshell? An n subshell?Draw, label, and explain the functions of the parts of a spectroscope.
- [p* L₂ da 0 HO H + →(a) Consider a wavefunction of the form: =1+x-1P7B.1 Imagine a particle confined to move on the circumference of a circle ('a particle on a ring'), such that its position can be described by an angle & in the range 0 to 2π. Find the normalizing factor for the wavefunctions: (a) e" and (b) eim, where m, is an integer.from x =0 tox = L. (b) What are the Si units of this unnormalized fur 2. (a) Determine the normalization constant for the particle in a box atypical wave function b which equais NyaL - 2 in the box from x-C tox=L and equals zero outside the box. You'll need to solve the integral below. (b) Explain how this function does (or does not) satisty the boum conditions for a particle in a box. 1= *dz here if the narticle is an electron, the sphere has a radlusE7D.5(b) Calculate the probability that a particle will be found between 0.65L and 0.67L in a box of length L for the case where the wavefunction is (i) ₁, (ii) V₂. You may make the same approximation as in Exercise E7D.5(a). pr E7 po pr9. The ground-state wavefunction for a particle confined to a one-dimensional box of length Lis 1/2 TCX L L Suppose the box is 10.0 nm long. 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. sin enWhich of the following functions are eigenfunctions of the momentum operator? a)eikx, b)eax2, c)x, d)x2, e)ax+b, d)sin(x+3a)Give the corresponding eigenvalue if appropriate.J J 8a. What is the expectation value of the linear momentum for the 1-D wavefunction: -ax² (x)= Ne where 0A particle freely moving in one dimension x with 0 ≤ x ≤ ∞ is in a state described by the normalized wavefunction ψ(x) = a1/2e–ax/2, where a is a constant. Evaluate the expectation value of the position operator.SEE MORE QUESTIONSRecommended textbooks for youPhysical ChemistryChemistryISBN:9781133958437Author:Ball, David W. (david Warren), BAER, TomasPublisher:Wadsworth Cengage Learning,Principles of Instrumental AnalysisChemistryISBN:9781305577213Author:Douglas A. Skoog, F. James Holler, Stanley R. CrouchPublisher:Cengage LearningIntroductory Chemistry: A FoundationChemistryISBN:9781337399425Author:Steven S. Zumdahl, Donald J. DeCostePublisher:Cengage LearningPhysical ChemistryChemistryISBN:9781133958437Author:Ball, David W. (david Warren), BAER, TomasPublisher:Wadsworth Cengage Learning,Principles of Instrumental AnalysisChemistryISBN:9781305577213Author:Douglas A. Skoog, F. James Holler, Stanley R. CrouchPublisher:Cengage LearningIntroductory Chemistry: A FoundationChemistryISBN:9781337399425Author:Steven S. Zumdahl, Donald J. DeCostePublisher:Cengage Learning