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 -oli

Harry Kroto 2004 Rayleigh Scattering

Bill Madden

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

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 = -1 transitions have the highest probability.

Hydrogen Atom Spectrum Harry Kroto 2004 E = - n2n2 R

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 Md 2 m1m1 m2m2 ab d The Parallel Axis Theorem I’ = I + Md 2 where M = m 1 + m 2

General Method of Structure Determination for Linear Molecules We wish to determine r 2 the position of a particular atom (mass m 2 ) from the Center of Mass (C of M) m1m1 m2m2 ab 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 r 2 the position of a particular atom (mass m 2 ) from the Center of Mass (C of M) m1m1 m2m2 ab d For the substituted molecule the parallel axis theorem yields 1I’ = I* + (M + ∆m)d 2 2I’ = I +∆mr 2 2 3I* - I = ∆mr 2 2 – (M + ∆m) d 2 a is the axis of the normal molecule b is the axis of the substituted molecule r2r2 r1r1

m1m1 m2m2 ab d 1I’ = I* + (M + ∆m)d 2 2I’ = I +∆mr 2 2 3I* - I = ∆mr 2 2 – (M + ∆m) d 2 I 4m 1 r 1 = m 2 r 2 5M 1 (r 1 + d) = (m 2 + ∆ m )(r 2 – d) 6m 1 r 1 + m 1 d = m 2 r 2 – m 2 d + ∆mr 2 – ∆md 7d(m 1 + m 2 + ∆m) = ∆mr 2 8d = {∆m/(M + ∆m)}r 2

I* - I = {∆m - ∆m 2 / (∆m + M)} r 2 2 ∆I = μ*r 2 2 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 = cm -1 H-C≡C-DB = cm -1

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