a. Using the values of the parameters for CO in Table A.22 in Appendix A, find the reciprocal wavelength at the band center and the splitting between the lines of the fundamental band in the rigid rotor–harmonic oscillator approximation.
| Table A.22 Properties of Diatomic Molecules | |||||||
| Term/Unit: | \frac{D_{e}/hc}{cm^{−1}} | \frac{\widetilde{v} _{e}}{cm^{−1}} | \frac{\widetilde{v} _{e}x_{e}}{cm^{−1}} | \frac{\widetilde{B} _{e}}{cm^{−1}} | \frac{r_{e}}{\mathring{A} } | \frac{\widetilde{α} _{e}}{cm^{−1}} | \frac{\widetilde{\mathscr{D}_{e}}}{10^{−4} cm^{−1}} |
| ^{79}Br_{2}/^{1}Σ^{+}_{g} | 325.32 | 1.077 | 0.0821 | 2.281 | 0.000319 | 0.00021 | |
| ^{12}C^{16}O/^{1}Σ^{+} | 90544 | 2169.8 | 13.29 | 1.931 | 1.128 | 0.0175 | 0.0612 |
| ^{35}Cl_{2}/^{1}Σ^{+}_{g} | 559.7 | 2.68 | 0.2440 | 1.988 | 0.0015 | 0.000186 | |
| ^{1}H_{2}/^{1}Σ^{+}_{g} | 38297 | 4401.2 | 121.3 | 60.85 | 0.741 | 3.06 | 0.00471 |
| ^{1}H^{81}Br/^{1}Σ^{+} | 2648.98 | 45.22 | 8.4649 | 1.414 | 0.233 | 3.46 | |
| ^{1}H^{35}Cl/^{1}Σ^{+} | 37240 | 2990.9 | 52.8 | 10.593 | 1.275 | 0.307 | 5.32 |
| ^{1}H^{19}F/^{1}Σ^{+} | 4138.3 | 89.9 | 20.956 | 0.9168 | 0.798 | 21.51 | |
| ^{1}H^{127}I/^{1}Σ^{+} | 2309.01 | 39.64 | 6.4264 | 1.609 | 0.1689 | 2.069 | |
| ^{127}I_{2}/^{1}Σ^{+}_{g} | 12550 | 214.5 | 0.615 | 0.03737 | 2.666 | 0.000114 | 0.000042 |
| ^{14}N_{2}/^{1}Σ^{+}_{g} | 79890 | 2358.6 | 14.3 | 1.998 | 1.098 | 14.3 | 0.0576 |
| ^{14}N^{16}O/^{2}\Pi _{1/2} | 1904.20 | 14.075 | 1.67095 | 1.15077 | 0.0171 | 0.54 | |
| ^{16}O_{2}/^{3}Σ^{-}_{g} | 1580.2 | 11.98 | 1.4456 | 1.208 | 0.0159 | 0.0048 | |
| ^{19}F_{2}/^{1}Σ^{+}_{g} | 916.64 | 11.236 | 0.89019 | 1.41193 | 0.013847 | 0.033 | |
| Data primarily from K. P. Huber and G. Herzberg, Molecular Spectra and Molecular Structure, Vol. IV, Constants of Diatomic Molecules, Van Nostrand Reinhold, New York, 1979. | |||||||
b. Find the value of the force constant k for the CO molecule.
c. Assuming that all transition dipole moments are equal and that the temperature is 298 K, find the most intense line in the P branch and in the R branch of the fundamental band.
