Question

Consider a CO molecule. The reduced mass is 1.14 x 10-26 kg. a) In Co the l = 0 to l = 1 rotational absorption line occurs at a wavelength of 2.6 mm (or frequency f = 1.15 x 1041 Hz). What is the bond length R (or equilibrium distance between the 2 atoms) of the CO molecule? b) When CO is dissolved in liquid carbon tetrachloride, infrared radiation of wavelength 4.67 um (or frequency f = 6.42 x 103 Hz) is absorbed. This absorption is due solely to the Co molecules being excited to the next higher vibrational state (disregard the carbon tetrachloride which is transparent to energy of this wavelength). What is the force constant k (or spring constant) of the bond in the CO molecules?

Answer 1

Rotational energy level Er= t(x+1) 872I for lao Ex=o. lol Era h2 872 r22 . of Photon The energy Es h² 417² My2 6.626x1034 ra - 402MY 472 x blux10 26x 1:15 X10 - 1:28x1020 .. The bond length r=v1:28x1020 21.315x1010 = 1.315 A rgstrom Now vibrational enery Level Eve (m+2) ħw ħwand =hy 20 M K = 25V VM u ir 24 = 407? (6.42x10²) x 1.24x102 = 1854.96 N/m Constart ~ 1855 N/m. Spring