CHM 374 Spring 2010 HOMEWORK SET 4 Due Wed., Feb. 17th (in class) Read Understanding Physical Chemistry ( UPC ), Chapter 6, Section 6.1 1. a) Use the particle-in-a-box energy formula (eq. 6.6) ) 8 /( 2 2 2 mL h n E n , to obtain an expression for the wavelength of a photon required to induce a particle-in-a-box to undergo a transition from n i to n f , expressed as a function of m and L (and other constants). b) Predict the wavelength (in nm units) of a photon which would be required to promote an electron from a state with n=5 to n=6, if it is confined within a one-dimensional box potential of 1 nm length. 2. Use the particle-in-a-box model to estimate the average carbon-carbon bond length of hexatriene, given that its experimental optical absorption wavelength is ~ 250 nm. 3. Use the particle-in-a-ring model to estimate the carbon-carbon bond length of benzene, given that its experimental optical absorption wavelength is ~200 nm. 4.
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