1. Determine whether the ground state function for the hydrogen atom is an eigenfunction of each of the following three operators. You should show this mathematically. a) kinetic energy operator for H atom b) potential energy operator for H atom c) Hamiltonian operator for H atom
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- Why does the wavefunction 4,4,0 not exist? Similarly, why does a 3f subshell not exist? See exercise 11.73 for notation definition.An official baseball has a mass of 145g. a Assuming that a baseball in New Orleans Superdome width =310m is acting as a particle-in-a-box, what is its energy in the n=1 state? b Assuming that the energy in part a is all kinetic energy (=12mv2), what is the velocity of the baseball in the n=1 state? c A hit baseball can travel as fast as 44.7m/s. Calculate the classical kinetic energy of the hit baseball and, assuming that this energy is quantized, determine the quantum number of the hit baseball.Is the uncertainty principle consistent with our description of the wavefunctions of the 1D particle-in-a-box? Hint: Remember that position is not an eigenvalue operator for the particle-in-a-box wavefunctions.
- For the system in exercise 9.1, determine the Hamiltonian equation of motion.An electron is confined to a box of dimensions 2A3A5A. Determine the wavefunctions for the five lowest energy states.a Construct Slater determinant wavefunctions for Be and B. Hint: Although you need only include one p orbital for B, you should recognize that up to six possible determinants can be constructed. b How many different Slater determinants can be constructed for C, assuming that the p electrons spread out among the available p orbitals and have the same spin? How many different Slater determinants are there for F?
- A particle on a ring has a wavefunction =eim, where =0to2 and m is a constant. a Normalize the wavefunction, where d is d. How does the normalization constant depend on the constant m? b What is the probability that the particle is in the ring indicated by the angular range =0to2/3? Does this answer make sense? How does the probability depend on constant m?Why does the concept of antisymmetric wavefunctions not need to be considered for the hydrogen atom?Graph the first five wavefunctions for the harmonic oscillators and their probabilities. Superimpose these graphs on the potential energy function for a harmonic oscillator and numerically determine the x values of the classical turning points. What is the probability that an oscillator will exist beyond the classical turning points? Do plots of the probability begin to show a distribution as expected by the correspondence principle?
- A 25-kg child is on a merry-go-round/calliope, going around and around in a large circle that has a radius of 8meters. The child has an angular momentum of 600kgm2/s. a From these facts, estimate the approximate quantum number for the angular momentum the child has. b Estimate the quantized amount of energy the child has in this situation. How does this compare to the childs classical energy? What principle does this illustrate?(QUANTUM CHEMISTRY) Dscribe how a wavefunction summarizes the dynamical properties of a system and how those properties may be predicted. Discuss the relation between probability amplitude, probability density, and probability. Describe the constraints that the Born interpretation puts on acceptable wavefunctions. What are the advantages of working with normalized wavefunctions?Calculate the energies of an electron in the fourth, fifth, and sixth energy levels of the Bohr nydrogen atom. Calculate the angular momenta of an electron in the fourth, fifth, and sixth energy evels of the Bohr hydrogen atom.