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CHAPTER II

Microwave Spectroscopy. CHAPTER II. The rotation of Molecules. There are two types of the molecular motion,The Linear motion or Circular motion. A body has three principle moments of inertia, one about each axis, usually designed as IA,IB and IC.

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CHAPTER II

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  1. Microwave Spectroscopy CHAPTER II The rotation of Molecules • There are two types of the molecular motion,The Linear motion or Circular motion. Molecular Spectroscopy (Chem442)

  2. A body has three principle moments of inertia, one about each axis, usually designed as IA,IB and IC. • ** Molecules may be classified into groups according to the relative valances of their • three principle moments of inertia. Molecular Spectroscopy (Chem442)

  3. Molecular Spectroscopy (Chem442)

  4. Molecular Spectroscopy (Chem442)

  5. Molecular Spectroscopy (Chem442)

  6. ROTATIONAL SPECTRA The Rigid Diatomic Molecule ro= r1 +r2 m1 r1 = m2r2 The moment of inertia about C is defined by I = m1 r12 + m2r22 Molecular Spectroscopy (Chem442)

  7. I=  ro2 •  = m1 m2 • m1 + m2 • By the use of the Schrödinger equation it may be shown that the rotational energy levels allowed to the rigid diatomic molecule are given by the expression: • Ej = h2 j(j+1) joules • 82 I Where j = 0,1,2,…… Molecular Spectroscopy (Chem442)

  8. J is the rotational quantum number (which can take integral values from zero to upwards). •  =E/h Hz • =E/hc cm-1 • j= Ej = h j(j+1) cm-1 • hc 82IC • j = 0,1,2,…… Molecular Spectroscopy (Chem442)

  9. B = h cm-1 • 82IC • j = Bj(j+1) cm-1 • J J+1 =2B (J+1) cm-1 • Selection rule: J=±1 Molecular Spectroscopy (Chem442)

  10. If we imagine the molecule to be in the j=0 state, we can let incident radiation be absorbed to raise it to the j=1 state. Plainly the energy absorbed will be: j= 1 - j= 0 = 2B -0=2B cm-1 And therefore, J=0 J=1 =2B cm-1 An absorption line will appear at 2B cm-1. If now the molecule is raised from the j=1 to the j=2 level by the absorption of more energy, we see immediately: J=1 J=2 =1= 2 - J= 1 = 6B -2B =4B cm-1 In general to raise the molecule from the state j j+1, we would have: j j+1 =B(J+1)(J+2)-BJ(J+1) = B [J2 +3J+2- (J2+J)] J J+1 =2B (J+1) cm-1 Molecular Spectroscopy (Chem442)

  11. Molecular Spectroscopy (Chem442)

  12. Problem • The first rotational line of CO occurs at 3.84235 cm-1. Calculate the moment of inertia and bond length of CO? The relative atomic weights (H=1.0080) to be C=12.000, O=15.9994, and the absolute mass of hydrogen atom to be 1.67343  10-27 kg, • Solution • 0 1 =3.84235 =2B cm-1 • B=1.921 cm-1 • B = h cm-1 I=h/82BC, so • 82 IC • ICO= 6.626  10-34 = 27.9907 10-47 = kg.m2 • 82 1.67343  10-27 B B • =14.56954 10-47 kg m2 •  = 19.92168 26.561 10-54 = 11.38356  10-27 kg • 46. 48303  10-27 • r2 = I/ = 1.2799  10-20 m2 • rco =0.1131 nm or (1.131) Molecular Spectroscopy (Chem442)

  13. The Effect of Isotopic Substitution • When a particular atom in a molecule is replaced by its –an element identical in every way except for its atomic mass- the resulting substance is identical chemically with the original. In particular there is no appreciable change in inter-nuclear distance on isotopic substitution. • 12C 13C • B B- • So, B  B- Molecular Spectroscopy (Chem442)

  14. Molecular Spectroscopy (Chem442)

  15. It is noteworthy that the data obtained from rotational spectra of a certain molecules can be used also for: • 1- Determination of the isotopes atomic weight. • 2- Microwave studies can give directly an estimate of the abundance of isotopes by comparison of absorption intensities. • 3- Determination of the bond length • - Molecular Spectroscopy (Chem442)

  16. Exercise 1. Calculate the frequency (in MHz) of the J= 4-3 transition in the pure rotational spectrum of 14N16O. The equilibrium bond length is 115 pm. 2. Given that the spacing of lines in the microwave spectrum of 27Al1H is constant at 12.604 cm-1, calculate the moment of inertia and bond length of the molecule. 3. Which of the following molecules may show a pure rotational microwave absorption spectrum: H2, HCl, CH4, CH3Cl, CH2Cl2. Molecular Spectroscopy (Chem442)

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