Substitution Structure

Scattering Theory

P = α E

Rayleigh Scattering

Clouds

Harry Kroto 2004

H 21 cm Line

Harry Kroto 2004

this shows a Hertz osci http://en.wikipedia.org/wiki/File:Dipole.gif

-oli

Harry Kroto 2004

Rayleigh Scattering

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

Bill Madden 559 2123

Attenuation due to scattering by interstellar gas and dust clouds

Harry Kroto 2004

ProblemsAssuming 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 = -1 transitions have the highest probability.

Hydrogen Atom SpectrumHarry Kroto 2004

E = - n2R

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

m1 m2

a b

d

The Parallel Axis Theorem

I’ = I + Md2 where M = m1 + m2

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)

m1 m2

a b

d

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

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)

m1 m2

a b

d

For the substituted molecule the parallel axis theorem yields

1 I’ = I* + (M + ∆m)d2

2 I’ = I +∆mr22

3 I* - I = ∆mr22 – (M + ∆m) d2

a is the axis of the normal molecule

b is the axis of the substituted molecule

r2r1

m1 m2

a b

d

1 I’ = I* + (M + ∆m)d2

2 I’ = I +∆mr22

3 I* - I = ∆mr22 – (M + ∆m) d2 I

4 m1r1 = m2r2

5 M1(r1 + d) = (m2 + ∆m)(r2 – d)

6 m1r1 + m1d = m2r2 – m2d + ∆mr2 – ∆md

7 d(m1 + m2 + ∆m) = ∆mr2

8 d = {∆m/(M + ∆m)}r2

I* - I = {∆m - ∆m2/ (∆m + M)} r22

∆I = μ*r22

where μ* = M∆m/(M + ∆m)

The reduced mass on substituion

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

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