CHEM4591 T 9 - CHEM4591 T 9-11:50am Feb 8th Weifeng Wang...

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CHEM4591 T 9-11:50am Feb 8th Weifeng Wang Partner: Zheng Zheng TA: Samuel Park Vibration-Rotation Spectrum of HCl Abstract The vibration-Rotation spectrum of HCl was measured by the fundamental spectrum and overtone spectrum. The fundamental spectrum was run on the FT-IR instruments, and the overtone spectrum was run on the Cary 17 instrument. The B’ we obtained for Cl 35 was 9.82 cm -1 , with an error of 6%. The B” for Cl 35 was 10.42 with an error of 2%; the B e was10.55, with an error of 0.4%; the r e was 1.28, with an error of 0.7%; ϖ e χ e was 49.5 cm -1 , with an error of 6%; the D was 44910 cm -1 , with an error of 25.7%. Introduction When a molecule absorbs light, its internal energy increases by the photon energy hv. The energy that the molecule obtained is used to excite the molecule’s electronic, vibration, and rotation state. In this experiment HCl molecules are used for analysis of their vibration-rotation spectrum. Two methods were employed to obtain the spectrum: one is the Cary 17 spectrophotometer for the first over tone spectrum, and the other is the FTIR instrument for the fundamental spectrum. Two basic theories---rigid rotor and harmonic oscillator-- are always used to approach the ideal light absorption. For diatomic molecules, the energy of rotation is calculated by 1
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E J = BJ(J+1) J = 0,1,2. .. (1) Here B is the rotational constant, and J is the rotational quantum number. B is described as, B = h/(8π 2 cμr 2 ) (2) In this equation, h is the Planck constant; c is the velocity of light; r is the H-Cl bond length; μ is the reduced mass, given by, μ = M 1 M 2 /(M 1 + M 2 ) (3) According to Hook’s law and Schrödinger’s equation, the energy of vibration is illustrated as, E v = ħω(v + ½) (v = 0, 1, 2, …) (4) In this equation, ħ is h/2 π , and ω is the angular frequency. Usually, it is convenient to introduce a spectroscopic constant with units of cm -1 . Dividing the energy by hc, a new equation in terms of ω e is used, E V = ω e (v+1/2) (5) Where ω e =ħω/hc = ω/2πc. However, these equations must be corrected before applying them to the real
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CHEM4591 T 9 - CHEM4591 T 9-11:50am Feb 8th Weifeng Wang...

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