# 1. A fictitious rotational absorption spectrum for 127179Br in its...

## Transcribed Text

1. A fictitious rotational absorption spectrum for 127179Br in its vibrationless ground state is shown below. 10 9 8 7 6 5 4 3 2 1 o 5 10 15 20 25 Transition Energy (cm-1) a. Determine the equilibrium bondlength of 1271"Br assuming it behaves as a rigid rotor. b. Determine the temperature of the 1271 Br sample. c. Assuming that IBr behaves as a harmonic oscillator, sketch/plot what the rotational absorption spectrum for 127181Br in its vibrationless ground state would look like if it were at the same temperature as the 271"Br sample. 2. Due to the significantly different frequencies for vibrational and rotational motions, the temperatures characterizing the populations in the vibrational and rotational states are most often independent of each. (Since they' re higher energy, vibrations take longer to thermally equilibrate and so the "vibrational temperature" is often higher than the "rotational temperature"). Assuming a vibrational temperature of 50 K and a rotational temperature of 10K, please sketch/plot what the v = 0 v' = 1 and V = 1 v'= 2 ro-vibrational absorption spectra of 23Na1271 would look like. Treat the vibrations as an anharmonic oscillator with ve =258.0 cm³ and Xeve = 1.035 cm-1 and the rotations as a rigid rotor with an equilibrium bondlength of 2.71145 A. 3. The harmonic oscillator, rigid-rotor wavefunctions are usually pretty accurate approximations for the wavefunctions of a diatomic molecule lying low within a potential well, even though the energies may be better represented by that for an anharmonic, rigid rotor. What would the harmonic oscillator, rigid rotor wavefunctions be for 14N16 if it were treated in this manner when in a state with an energy of 8294.111 cm'1? Give at least 3 possibilities. The vibrational constants for 14N16 are ve = 1904.20cm and XeVe = 14.075 The rigid rotor equilibrium bondlength is 1.15077 Ä.

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