Engineering Chemistry Module I- Molecular Spectroscopy PDF

ENGINEERING CHEMISTRY Lata Pasupulety Department of Science and Humanities ENGINEERING CHEMISTRY Module I- Molecular Spectroscopy Class content: Expression for rotational energy levels of a diatomic molecule Selection rules Rotational spectrum  ENGINEERING CHEMISTRY Module...

ENGINEERING CHEMISTRY Lata Pasupulety Department of Science and Humanities ENGINEERING CHEMISTRY Module I- Molecular Spectroscopy Class content: Expression for rotational energy levels of a diatomic molecule Selection rules Rotational spectrum  ENGINEERING CHEMISTRY Module I- Molecular Spectroscopy Expressions for rotational energy levels for a Derivation of Moment of Inertia for a heteronuclear diatomic molecule diatomic molecule- rigid rotor model Source:Fundamentals of Molecular Spectroscopy: C. N. Banwell and Elaine M McCash, Fifth Edition, MCGRAW- HILL Education (India) Private Ltd. A rigid diatomic molecule with masses m1 and m2 joined by a thin rod of length r 0 = r1 + r2.The centre of mass is at C ENGINEERING CHEMISTRY Module I- Molecular Spectroscopy The molecule rotates end- over- end about a point C, the centre of gravity , this is defined by the moment, or balancing, equation: m1 r1 m2 r2 The moment of inertia about C is defined by I = m1r12 + m2r22 I m2 r2 r1  m1 r1r2 I r1 r2 (m1  m2 ) m2 ro Since , r1  m1  m2 mr Since , r2  1 o m1  m2 mm Therefor I  1 2 ro 2 ro 2 e m1  m2 m1 m2  Where μ is the reduced mass m1  m2 given by  ENGINEERING CHEMISTRY Module I- Molecular Spectroscopy 1 E  I  L r 2 2 Rotational energy 2 2I ; Since L=Iω Solving the Schrodinger equation for a rigid rotor shows that angular momentum is quantised and is given by, h where J is the rotational quantum number. The quantity J , rotational quantum number, which can take integral values from zero upwards; J=0,1,2,3...... Hence the rotational energy levels are quantised and given by the expression, h2 EJ  J ( J  1) Joules 8 2 I Planck’s constant=6.626×10-34 Js and I is the moment of inertia  ENGINEERING CHEMISTRY Module I- Molecular Spectroscopy The energy expressed in spectroscopic units(cm ) is given -1 by : h 1  BJ ( J  1)cm  1   2 J ( J  1)cm which can be written J J 8 Ic as h where 2 cm  1 B 8 Ic B is known as the rotational constant Substituting for values of J = 0,1,2,3..., we can get the energies for the rotational J εJ levels 0 0 1 2B 2 6B 3 12B Source:Fundamentals of Molecular Spectroscopy: C. N. Banwell and Elaine M McCash, Fifth Edition, MCGRAW-HILL Education (India) Private Ltd.  ENGINEERING CHEMISTRY Module I- Molecular Spectroscopy The selection rules for rigid rotor model obtained after solving Schodinger equation is : Gross selection rule – molecule should possess permanent dipole moment ΔJ=±1  J BJ ( J  1)cm  1 Since For rotational transition  J ( J 1)  of 2 a B(molecule J  1)cm  1 from level J  J +1 , the energy absorbed is given by Substituting for values for J = 0,1,2,3.... J Δε(JJ+1) 0 2B cm-1 1 4B cm-1 2 6B cm-1 ENGINEERING CHEMISTRY Module I- Molecular Spectroscopy Rotational energy levels and spectrum J Δε(JJ+1) 0 2B cm-1 1 4B cm-1 2 6B cm-1 3 8B cm-1 4 10B cm-1 Source:Fundamentals of Molecular Spectroscopy: C. N. Banwell and Elaine M McCash, Fifth Edition, MCGRAW- HILL Education (India) Private Ltd.  ENGINEERING CHEMISTRY Module I- Molecular Spectroscopy Information obtained from the rotational spectrum Source:http:// www.physics.dcu.ie/~be/ Ps415/Rotational1.pdf The first line in the spectrum appears at 2B cm-1 and the distance between any two consecutive lines is constant and is equal to 2B cm-1. We can get value of ‘B’ from the spectrum and calculate h ,I, the moment of inertia using the 1 expression B  2 cm 8 Ic Since I = µ ro2 , ro can be determined ; ro is the bond length of the molecule The spectrum also reveals that some higher rotational levels are also populated at room temperature THANK YOU Lata Pasupulety Department of Science and Humanities [email protected] +91 80 6666 3333 Extn 759