Question

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NAME Physical Chemistry Test 2 Instructions: Do FIVE of the following problems Your best problem will be graded out of points Your third best will be graded out of 20 points Your fifth best will be graded out of 10 peints f30 pointsYour second best will be graded out of 25 points Your fourth best will be graded out of 15 points 1. The work function of uranium is 3.73 ev a. Caculate the maximum photon wavelength needed to eject an electron from uranium. b. Find the velocity and de Brogle wavelength of an electron ejected from uranium with a 2200 nm photon 2. The Bluackbody temperature" of a planet is that predicted by the central wavelength of the blackbody emission a. Predict the blackbody temperature of Mars if the central wavelength is 12.6 micrometers. them) micrometer 10* m). b. Estimate the energy spectral density (p,Tl using both the Rayleigh-Jeans law and the Planck distributions 3. In a butadiene molecule (shown below) the pi electrons are conjugated over three bonds, which can be approximated as a particle in a box. Calculated the wavelength of light needed to excite an electron from the nezto n-3 level, taking the box length to be 7.0 Angstroms 4. One function with satisfies the boundary conditions for particle in a 1-dimensional box of length L i Find the value of the normalization constant N (in terms of L). 5. Give the energy of a proton in a 3-D box with three equal sides of L-5.00 Angstroms and n,-1, n,-2, and n-3 How many energy levels (as defined by a set of quantum numbers (nnn)are degenerate with this one? 6. Show that the wavefunctions for a 1D particle in a box for the n 1 and ne2 levels are orthogonal to each other 7. Find the average value (in terms of L) for x2 for a particle in a 1D box with ne1. 8. For ne2, find the probability that a particle in a 1D box is between 3'L/4 and L/4 9. In the following table, give the eigenvalue if the function is an eigenfunction of that operator. If it is not, write "no" dx dx2 3e* cos X-sinx 10. Show whether the operators (1/x)* and d/dx commute by having them act on an arbitrary function f(x)

Answer 1

Wavetunui on of 1-D box 8- sin(n*) 2 Sin when n: 2 From the condition orthogonality, we have Follosing the e

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