I don't need these questions answered to completion just some guidance in the right direction. I am not receiving help from my TA for these dry lab questions. The tabulated data mentioned in the problem is shown in the figure shown on the bottom in cm^-1.
5. From the tabulated data, determine the spectroscopic constants o, Be, and de from a linear regression analysis of equations (17) and (18). Also do this by calculation of the consecutive differences in the P and R branch lines (equations (21) and (22)). From these analyses, you should obtain multiple redundant values of , Be and de. Now use the best values to obtain the moment of inertia, I, of HCl. From the reduced mass, obtain a value for re. 6. Using your values of Be and o, calculate D, the centrifugal distortion constant (equation (10)). What must the value of J be for the centrifugal distortion term to be 1% of the rigid rotator term in equation (10)? Does this result justify ignoring D in your experimental results? 7. Assuming that the Q-branch could be represented, if present, by a single line, calculate the frequency of this line from your spectral data and compare this value to the observed center of the R and P branches in your HCl spectrum. 8. The force constant for H35Cl is 5.1669 x 105 dynes cm" (ergs cm). What are the expected values of , and the anharmonicity constant? (Do values are given in Table 13.2 in the textbook.) 9. In general, what accounts for the uneven spacing on the lines in the P and R branches of a vibration-rotation spectrum? Be = h 872cur2 (8) Ev,J= (v+1/2)hc 7,- (v+1/2)?hc xe + J(J+1)hcBe - J?(5+1)?hcD (11) In this experiment, we are justified in neglecting centrifugal distortion, and thus we will neglect the last term in equation (11). However, the complete separation of rotational and vibrational motion is not realistic because the mean internuclear separation depends on the degree of vibrational excitation (i.e., v), and the rotational constant is a function of 1/72 [see equation (8)]. The "effective" rotational constant for a vibrating molecule will vary with the mean value of 1/r for the vth eigenstate, i.e., v. The rotational constant can be approximated by 4 B, B. - Oc(v + 1/2) (12) where By is the rotational constant taking vibrational excitation into account, and ae is defined as the rotational-vibrational coupling constant. It turns out that for an anharmonic potential (e.g. the Morse potential), de> 0, whereas for the harmonic potential, ac (P2), etc. Likewise, for the successive differences in the R-branch lines, i.e., R1 - RO; R2 -Ri, etc., the result is R(J" + 1) - R(J") = A VR= 2Bc - 50c - 2a.J J = 0,1,2, .... (22) ved J=0 P R 2 Figure 1 (repeated): Allowed transitions are shown as solid lines, while forbidden transitions are dashed lines. The length of the arrow (spacing of the levels) corresponds to the energy difference between the initial and final level. 2842.99 2820.96 0.55 2942.53 2923.54 2841.49 2819.47 2798.42 0.50 2960.94 294438 2962.74 2796.86 2925.38 0.45 2980.47 2775.33 2773.61 2978.53 0.40 2862.89 2997.52 2905.83 2864.54 2750.00 0.35 3013.97 2995.53 2751.52 0.30 3029.69 3011.94 2725.72 0.25 3044.68 2727.43 3027.51 2903.98 2701.01 0.20 3042.49 3058.96 2702.58 2675.80 0.15 3072.48 3056.78 2677.43 0.10 2651.56 2883.97 0.05 3085.34 2625.43 0.00 -0.030 3150.0 3100 3000 2900 2800 2700 2600.0 cm-1 c:\pel_datalspectralmacalady hcl2done sp 5. From the tabulated data, determine the spectroscopic constants o, Be, and de from a linear regression analysis of equations (17) and (18). Also do this by calculation of the consecutive differences in the P and R branch lines (equations (21) and (22)). From these analyses, you should obtain multiple redundant values of , Be and de. Now use the best values to obtain the moment of inertia, I, of HCl. From the reduced mass, obtain a value for re. 6. Using your values of Be and o, calculate D, the centrifugal distortion constant (equation (10)). What must the value of J be for the centrifugal distortion term to be 1% of the rigid rotator term in equation (10)? Does this result justify ignoring D in your experimental results? 7. Assuming that the Q-branch could be represented, if present, by a single line, calculate the frequency of this line from your spectral data and compare this value to the observed center of the R and P branches in your HCl spectrum. 8. The force constant for H35Cl is 5.1669 x 105 dynes cm" (ergs cm). What are the expected values of , and the anharmonicity constant? (Do values are given in Table 13.2 in the textbook.) 9. In general, what accounts for the uneven spacing on the lines in the P and R branches of a vibration-rotation spectrum? Be = h 872cur2 (8) Ev,J= (v+1/2)hc 7,- (v+1/2)?hc xe + J(J+1)hcBe - J?(5+1)?hcD (11) In this experiment, we are justified in neglecting centrifugal distortion, and thus we will neglect the last term in equation (11). However, the complete separation of rotational and vibrational motion is not realistic because the mean internuclear separation depends on the degree of vibrational excitation (i.e., v), and the rotational constant is a function of 1/72 [see equation (8)]. The "effective" rotational constant for a vibrating molecule will vary with the mean value of 1/r for the vth eigenstate, i.e., v. The rotational constant can be approximated by 4 B, B. - Oc(v + 1/2) (12) where By is the rotational constant taking vibrational excitation into account, and ae is defined as the rotational-vibrational coupling constant. It turns out that for an anharmonic potential (e.g. the Morse potential), de> 0, whereas for the harmonic potential, ac (P2), etc. Likewise, for the successive differences in the R-branch lines, i.e., R1 - RO; R2 -Ri, etc., the result is R(J" + 1) - R(J") = A VR= 2Bc - 50c - 2a.J J = 0,1,2, .... (22) ved J=0 P R 2 Figure 1 (repeated): Allowed transitions are shown as solid lines, while forbidden transitions are dashed lines. The length of the arrow (spacing of the levels) corresponds to the energy difference between the initial and final level. 2842.99 2820.96 0.55 2942.53 2923.54 2841.49 2819.47 2798.42 0.50 2960.94 294438 2962.74 2796.86 2925.38 0.45 2980.47 2775.33 2773.61 2978.53 0.40 2862.89 2997.52 2905.83 2864.54 2750.00 0.35 3013.97 2995.53 2751.52 0.30 3029.69 3011.94 2725.72 0.25 3044.68 2727.43 3027.51 2903.98 2701.01 0.20 3042.49 3058.96 2702.58 2675.80 0.15 3072.48 3056.78 2677.43 0.10 2651.56 2883.97 0.05 3085.34 2625.43 0.00 -0.030 3150.0 3100 3000 2900 2800 2700 2600.0 cm-1 c:\pel_datalspectralmacalady hcl2done sp
