Question

4. Anharmonic potential (15 points) The adjacent figure shows the experimentally determined potential energy curve of the electronic ground state of"Br2, with a few of the vibrational levels. The vibrational transitions are reasonably well described by a harmonic oscillator model, but much more accurately by including a small anharmonic correction term: En/hcVe(n 1/2) - vexe(n + 1/2)2. From fits to experimental data, the values of the constants are 325.32 cm and exe 1.08 cm .5 10 15 (a) Calculate the energy (in cm1 equivalents) of the 0-> 1 vibrational transition both with and without the 2 2.5 3 3.5 r/ A 4.5 anharmonic correction. What is the difference, and which is smaller? (b) The above expression for the energy levels looks similar to the one for the Morse potential, which is e (n + 1/2)2, where D is the depth of the Morse potential well. By comparing this with the expression given above, calculate a value for De (in cm equivalents) (c) The actual value of De from the figure is Delhc = 16056875 cm-1. Explain the discrepancy between this value and the one you calculated assuming a Morse potential (d) How are the bond dissociation energy Do and the potential well depth De related? Calculate Do (in kJ/mol) using the correct value of De given under (c). Hint: Don't forget the anharmonic term.

Answer 1

1 2 2. Et h. C 48782.43

Date DELTA İPyAO 1)乙 S e o e ROUGH

DELIA 火_X2 Vexe A c lor&33.10 7.31 24498 3 C ch-