Physical Chemistry

2nd Edition

ISBN: 9781133958437

Author: Ball, David W. (david Warren), BAER, Tomas

Publisher: Wadsworth Cengage Learning,

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Suppose that the spin quantum number had three allowed values (ms=0,+12,12) . Give the atomic numbers of the first three noble-gas atoms in this case.

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Based on the trend shown in Figure 11.5, draw the probability distribution of a harmonic oscillator wavefunction that has a very high value of n. Explain how this is consistent with the correspondence principle.

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Using Table 5.2, write down the mathematical expression for the 2px wave function for an electronically excited H atom. Estimate the probability of finding the 2px electron if you look in a cubical box of volume of 0.8(pm)3 centered at a distance of 0.5001010m in the =/2 , =0 direction. Does this probability change as you change ? At what angles is the probability of finding the electron smallest and at what angles is the probability the largest? (Note that =2 is the same location as =0 , so don’t double count.)

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a For a pendulum having classical frequency of 1.00s1, what is the energy difference in J between quantized energy levels? b Calculate the wavelength of light that must be absorbed in order for the pendulum to go from one level to another. c Can you determine in what region of the electromagnetic spectrum such a wavelength belongs? d Comment on your results for parts a and b based on your knowledge of the state of science in early twentieth century. Why wasnt the quantum mechanical behavior of nature noticed?

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Identify measurable wave properties that are used in describing light.

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In the Stern-Gerlach experiment, silver atoms were used. This was a good choice, as it turned out. Using the electron configuration of silver atoms, explain why silver was a good candidate for being able to observe the intrinsic angular momentum of the electron. Hint: Dont use the aufbau principle to determine the electron configuration of Ag, because its one of the exceptions. Look up the exact electron configuration in a table.

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Explain why the wave model for radiation cannot account for the photoelectric effect.

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How many radial nodes and how many angular nodes does each of the orbitals in Problem 4 have?

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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?

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For the Li atom, the energy difference between the ground state and the first excited state, in which the outermost electron is in a 2p orbital, is 2.961019J . In the Li2+ ion, the energy difference between the 2s and 2p levels is less than 0.00002 of this value. Explain this observation.

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Sketch the major features (number of peaks and relative intensities for the peaks) of the expected photoelectron spectrum for atoms of nitrogen.

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The wave function of an electron in the lowest (that is, ground) state of the hydrogen atom is (r)=( 1 a 0 3 )1/2exp(r a 0 )ao=0.5291010m (a) What is the probability of finding the electron inside a sphere of volume 1.0pm2 , centered at the nucleus (1pm=1012m) ? (b) What is the probability of finding the electron in a volume of 1.0pm2 at a distance of 52.9 pm from the nucleus, in a fixed but arbitrary direction? (c) What is the probability of finding the electron in a spherical shell of 1.0 pm in thickness, at a distance of 52.9 pm from the nucleus?

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