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Substitution Structure

This article discusses the substitution structure of hydrogen atom in scattering theory and explores the phenomenon of Rayleigh scattering in clouds. It also examines the size of a hydrogen atom and estimates the lifetimes of different states. Additionally, the parallel axis theorem and its application in determining the structure of linear molecules is explained.

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Substitution Structure

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  1. Substitution Structure

  2. P = α E Scattering Theory

  3. Rayleigh Scattering

  4. Clouds

  5. H 21 cm Line Harry Kroto 2004

  6. this shows a Hertz osci http://en.wikipedia.org/wiki/File:Dipole.gif-oli Harry Kroto 2004

  7. Rayleigh Scattering Harry Kroto 2004

  8. http://www.ccpo.odu.edu/~lizsmith/SEES/ozone/class/Chap_4/index.htmhttp://www.ccpo.odu.edu/~lizsmith/SEES/ozone/class/Chap_4/index.htm

  9. Bill Madden 559 2123

  10. Attenuation due to scattering by interstellar gas and dust clouds Harry Kroto 2004

  11. Problems Assuming the Bohr atom theory is OK, what is the approximate size of a hydrogen atom in the n= 100 and 300 states Estimate the lifetimes of these states assuming that the ∆n = -1transitions have the highest probability.

  12. R E = - n2 Hydrogen Atom Spectrum Harry Kroto 2004

  13. If I is the moment of inertia of a body about an axis a through the C of G the Parallel Axis Theorem states that the moment of inertia I’ about an axis b (parallel to a) and displaced by distance d (from a) is given by the sum of I plus the product of M the total mass and the square of the distance ie Md2 a b d m1 m2 The Parallel Axis Theorem I’ = I + Md2 where M = m1 + m2

  14. General Method of Structure Determination for Linear Molecules We wish to determine r2 the position of a particular atom (mass m2) from the Center of Mass (C of M) a b d m1 m2 I = Moment of Inertia of the normal species about a the C of M I* = Moment of Inertia of the substituted species about b its C of M I’ = Moment of Inertia of the substituted species about a

  15. General Method of Structure Determination for Linear Molecules We wish to determine r2 the position of a particular atom (mass m2) from the Center of Mass (C of M) a is the axis of the normal molecule b is the axis of the substituted molecule a b d m1 m2 r1 r2 • For the substituted molecule the parallel axis theorem yields • I’ = I* + (M + ∆m)d2 • I’ = I +∆mr22 • I* - I = ∆mr22 – (M + ∆m) d2

  16. I’ = I* + (M + ∆m)d2 • I’ = I +∆mr22 • I* - I = ∆mr22 – (M + ∆m) d2 I • m1r1 = m2r2 • M1(r1 + d) = (m2 + ∆m)(r2 – d) • m1r1 + m1d = m2r2 – m2d + ∆mr2 – ∆md • d(m1 + m2 + ∆m) = ∆mr2 • d = {∆m/(M + ∆m)}r2 a b d m1 m2

  17. I* - I = {∆m - ∆m2/ (∆m + M)} r22 ∆I = μ*r22 where μ* = M∆m/(M + ∆m) The reduced mass on substituion

  18. Problem Determine the bond lengths for the molecule H-C≡C-H H-C≡C-H B = 1.17692 cm-1 H-C≡C-D B = 0.99141 cm-1

  19. Queen Magazine

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