Vibrational (Raman) spectroscopic data gives the following information for ^14N_
ID: 503718 • Letter: V
Question
Vibrational (Raman) spectroscopic data gives the following information for ^14N_2: V =2358.6 cm^-1, v x_e = 14.324 cm^-1 and for ^16O_2; v = 1580.4 cm^-1, v x_e = 12.073 cm^-1. Calculate D_o for both (not D_e) assuming the Morse approximation to the vibrational potentials. ii) Draw the molecular orbital energy level diagrams of these molecules and indicate which orbitals are bonding and anti-bonding and which are occupied by electrons. Then, discuss the computed values of D_o in terms of the bond orders of the molecules you obtain from the MO diagrams. Sketch a Birge-Sponer plot for the vibrational potential of ^14N_2. Calculate the maximum value of v before the ^14N_2 bond will dissociate.Explanation / Answer
The energy equation for diatomic molecule is
En = (n+1/2)v-(n+1/2)2vxe -----> We ingnored the higher order corrections to the actual energy as the potential energy of a diatom is not a parabola (simple harmonic) but it is more close to Morse potentials.
(a) For 14N2 we have the data v = 2358.6 cm-1 and vxe = 14.324 cm-1
Substituting this data in the energy equation given above for n = 0 (ground vibrational level), we get
E0 = v/2 - (vxe)/4 = 2358.6/2 - (14.324)/4 = 1179.3 - 3.581 = 1175.719 cm-1
So the ground vibrational level of the 14N2 is 1175.719 cm-1
Now according the following equation,
De = v2/(4vxe) = (2358.6)2/(4x14.324) = 97092.187cm-1
Now, D0 = De - E0 = 97092.187-1175.719 = 95916.47 cm-1.
(b) For 16O2, v = 1580.4 cm-1 and vxe = 12.073 cm-1.
The ground vibrational level energy (puting n = 0 in the energy equation given in the top) we get
E0 = v/2 - (vxe)/4 = 1580.4/2 - 12.073/4 = 790.2 - 3.01825 = 787.18175 cm-1
Also, De = v2/(4vxe) = (1580.4)2/(4x12.073) = 51720.04 cm-1.
Now, D0 = De - E0 = 51720.04 - 787.18175 = 50932.86 cm-1.
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