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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?Consider a spin-1/2 atom with spins up and down. For a system of N such localized atoms, Find the number of configurations with excess spin S.
- Arsenic, with configuration 3p³, has the term symbols 2p, 2D, 4S. Find the possible J values for each of these, and match the appropriate set of J values with each term symbol. C. 2p E. 2D B. A. B. 4S 1123 312 c. 112 D. 112 512 312 E. 1/2. 312 512 ?The Hückel determinant for a 4 Carbon containing conjugated cyclic molecule has four roots as:-1.532089, -0.347296, 1.0 and 1.879385.(there are 4 t electrons Set up the Hückel determinant for the linear isomer of this molecule and solve for eigenvalues. Which molecule is more stable?How do the energy eigenstates of the 2D rigid rotor compare to (1) the eigenstates of a free particle and (2) the eigenstates of a particle in a box?
- a) The physical interpretation of the wavefunction and the fact that it is a solution of the Schroedinger equaton, which is a 2nd order differential equation, causes many restrictions on an acceptable wave function solution: (i) it must be single valued; (ii) it must be continuous; (iii) its slope must be continuous; and (iv) it must be normalizable or normalized. Sketch the following functions and check whether they can be wave function. Explain your answers. 1) 4(x) = for 0 < x <∞ 2) Y(x) = | sin(nx)|, for 0 < x< 2 3) Ҹ(x) %3D In (x), for 1 < x < 0o S0 for – 1 < x < 0 (1 for 09. Considering that spin state of a particle is known in the rest system of this particle, find bispinor u(p) in coordinate system, where the particle has momentum p. Using this result find connection between average values of spin vector of the particle in mentioned above coordinate systems. 10. Show that for Dirac particle with mass m=0 the operator ys commutes with Hamiltonian of the free particle. Find eigenvalues of this operator and explain their physical meaning.Consider the d' electron configuration of a free ion: a) Calculate the spin multiplicity b) Calculate the maximum value of ML, and deduce the value of L. c) Based on your calculation of S and L what is the term symbol of the d“ free ion?What is the degeneracy of a molecule rotating with J = 4?What is the maximum degeneracy of the wavefunctions of a particle confined to the interior of an octahedral hole in a crystal?The nuclear spin of deuterium, D, is I= 1. Calculatethe ratio of the number of ways of achieving rotational statesw ith odd and even values of J.SEE MORE QUESTIONS