chem5314_hwk5_soln - Chem 5314 homework #5 – out of 33...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Chem 5314 homework #5 – out of 33 marks Problem 1 – 10 marks Relative to the n = 0 vibrational level of the ground (X) electron state of 79 Br 2 , the vibrational levels (n) of the excited (B) state have energies (in cm- 1 ) as follows: (the table is taken from J. Mol. Spectroscopy 51 , 428 (1974), which is in the library; the symbols X and B are spectroscopic symbols we have not discussed in class) n E (cm- 1 ) 15823.47 1 15987.78 2 16148.73 3 16306.26 4 16460.33 5 16610.87 6 16757.83 7 16901.15 8 17040.78 9 17176.65 10 17308.65 11 17436.89 12 17561.14 13 17681.50 14 17797.88 15 17910.18 16 18018.37 17 18122.45 18 18222.46 19 18318.33 20 18410.07 21 18497.66 The dissociation limit (again relative to vibrational level n=0 of the ground (X) electronic state) is 19579.76 cm- 1 for the B state. 1 The harmonic oscillator has energy levels E n = ( n + 1 2 ) ~ ω The Morse potential has energy levels E n = ( ( n + 1 2 )- x e ( n + 1 2 ) 2 ) ~ ω where x e is the anharmonicity parameter, which is related to the depth of the well (for a Morse oscillator the well is not infinitely deep because the molecule can dissociate into separate atoms). How well does the data for the B state fit a harmonic approximation? How well does it fit the Morse approximation? You must do some kind of rigorous statistical analysis to quantify your answer. Solution: If we plot Δ E vs (n+1), the harmonic oscillator model gives a horizontal line (zero slope) with a y-intercept of ~ ω and the Morse oscillator model gives a straight line with a y-intercept of ~ ω and a slope of- 2 ~ ωx e . We can see this by doing the math: for the harmonic oscillator,...
View Full Document

This note was uploaded on 02/08/2012 for the course CHEM 5314 taught by Professor Nielsen during the Fall '11 term at University of Texas at Dallas, Richardson.

Page1 / 5

chem5314_hwk5_soln - Chem 5314 homework #5 – out of 33...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online