At low resolution, the strongest absorption band in the infrared absorption spectrum of ¹²C¹⁶O is centred at 2150 cm⁻¹. Upon closer examination at higher resolution, this band is observed to be split into two sets of closely spaced peaks, one on each side of the centre of the spectrum at 2143.26 cm⁻¹. The separation between the peaks immediately to the right and left of the centre is 7.655 cm⁻¹. Make the harmonic oscillator and rigid rotor approximations and calculate from these data:

(a) The vibrational wavenumber of a CO molecule,

(b) Its molar zero-point vibrational energy,

(c) The force constant of the CO bond,

(d) The rotational constant B, and

(e) The bond length of CO.