1. Carbon monoxide, Co, has an intense infrared absorption due to the large valu
ID: 1089280 • Letter: 1
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1. Carbon monoxide, Co, has an intense infrared absorption due to the large value of the dipole moment derivative, du/dRIR, , and the intensity of its IR absorption bands can be used as a means of measuring the temperatures of stellar atmospheres through vibrational spectroscopy. For this molecule, which has been studied for many decades, the vibrational constants are very precisely known: We = 2169.81358 cm' and weXe = 13.28831 cm. Higher-order anharmonic constants are also known, but will be ignored in this problem. (a). Based on the values of me and WXe given above, and assuming that the molecule follows the behavior of a Morse oscillator, estimate the bond dissociation energy, De. Convert your value to electron volts (1 eV = 8065.544 cm') and compare to the accepted value, D.= 11.291 + 0.004 eV. (b). Using the constants provided above, calculate the transition wavenumbers (cm) for the V=1V=0, v=2+v=1, v=2+v=0, and v=3+v=0 vibrational transitions. These transitions are usually labeled as the 1-0, 2-1, 2-0, and 3-0 bands, respectively. Note that the order is written so that the upper state is written first, followed by the lower state quantum number. For each transition, identify whether it is a fundamental band, a hot band, or an overtone band. (C). An astronomer records the infrared spectra of a star and observes absorptions due to the v=1+v=0 and v=2+v=1 transitions of Co, which is apparently present in the stellar atmosphere. The absorption strength of the v=2+v=1 transition is 0.6 times the strength of the v=l+v=0 transition. Assuming that this ratio is indicative of the fraction of molecules in the v=1 level, compared to the v=0 level, use the Boltzmann expression for this ratio, = exp(-(G(1) - G(0))/kT), to estimate the temperature of the atmosphere of the star. This is much cooler (a relative term !) than the temperature in the stellar interior. It will be helpful to know that Boltzmann's constant, kg, may be expressed as 0.69503 cm''/K. How does your result compare to the surface temperature of the sun, which is 5778 K?Explanation / Answer
(b) Transition wavenumber are v=1 <- v=0 is 2169.81358*(1-2*(13.28831/2169.81358)) cm-1.
Similarly, v=2<- v-1 is 2169.81358*(1-4*(13.28831/2169.81358)) cm-1.
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