Chemistry Assignment 4: Problems from Munowitz Ch. 2 & 6 and Lecture Notes (Winter 2001), Assignments of Chemistry

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CHEM 20A. Winter 2001 Assignment 4.

Read Munowitz Chapter 6 (already assigned); Chapter 2. Sections 2.3, 2.4, 2.5. Read Lecture Notes. Through lecture notes set #11. Problems: (Due Feb. 14: in TA boxes). Remember that starred problems must be handed in. Asssigned problems In Munowitz: already assigned but need not be turned in. (This stars only indicate that they are particularly important).. 6.5, 6.9, 6.29, 6.35, 6.36, 6.37* New in Munowitz. 2.12, 2.16, 2.18, 22.33, 2.36, 2.40. Special Problems. 9.1, 9.2, 9.3, 10.2, 11.1, 11.2*

SPECIAL PROBLEMS. SET #

9.1. Diffraction For good diffraction experiments one wants wavelengths to be of the order of an Å or so. a) Why? b) What energy (in eV) should a beam of electrons have in order to have a 1Å wavelength? c) What energy (in eV) should a beam of neutrons have in order to have a wavelength of 1Å?

9.2 Diffraction. In Young's famous two slit experiment, light from a source passes through the two slits in a screen , and falls on a photosensitive detector. One observes alternate bright and dark spots at the detector. The beam from the lower slit travels farther and so oscillates more on its way to points above the center than does the beam from the upper slit. For bright spots, the difference in path lengths must be λn, where n is an integer. The formula for the bright spots is then nλ = dsinθ. Derive this and a similar formula for the dark spots.

9.3 Diffraction. In an atomic crystal the atoms are arranged in a fixed array. The distance between planes is d. If a beam comes in at an angle θ to the plane and the scattered light is detected at the same angle, the part scattering off the second plane of atoms travels a distance 2dsinθ farther than that scattering off the surface plane. a) Prove this if you can. One then finds a bright spot (high scattering intensity) if the beam comes in at angle θ determined by 2dsinθ = nλ , where n is an integer and λ is the wavelength. b) Prove this. This formula is known as the Bragg formula and the angle is the Bragg angle. c) How can the Bragg formula be used in studies of molecular structure? c) Why should λ be comparable to d for good diffraction results?

10.2* Dimensional Analysis.

i) Obtain the expression, ro is proportional to 4πεoh^2 /me2Z, for the characteristic length scale ro in a hydrogen-like atom. ii) Explain why the only relevant dimensional constants are those in this expression. iii) Argue why this is the only characteristic length scale, i.e. why all interesting lengths should be roughly this length.

11.1* Energy level diagram and Ionization. a) Draw an energy level diagram with the

ε1s orbital energies levels for the following atoms and ions: H, He+, Li2+, He, Li+, Li. The depth (below zero) for each ε1s should be in the correct order, and the approximate relative value of each should be indicated. Explain carefully your reasoning in obtaining these results. Indicate the approximate relative values of the first ionization energies for the following atoms and ions: H, He+, Li2+, He, Li+, Li. Explain carefully your reasoning in obtaining these results.

b) Indicate the approximate ratio of the energy needed to remove a 2s electron from Li to that needed to remove a 1s electron. Explain carefully your reasoning in obtaining these results. [Both processes are single ionization processes, removing the 2s electron is what is normally called first ionization and removing a 1s electron is called ionization of an inner or core electron].

c) Draw an approximate energy level diagram with the 1s and 2s levels of He in its ground state (1s)^2 , and draw a similar diagram for He in its first excited state (1s)(2s). Explain carefully your reasoning in obtaining these results.

11.2* Spectra. A photon of the correct frequency can cause an electronic transition from the 1s to the 2p level. Draw (qualitatively) a spectrum for an equimolar mixture of H, He+, and He atoms.