Bill Madden

 = (4  /3ħc)  n  e  m  2  (N m -N n )  (  o -  ) Square of the transition moment  n  e  m  2 2.Frequency of the light  3.Population difference (N m - N n ) 4.Resonance factor - Dirac delta function  (0) = 1

 = (4  /3ħc)  n  e  m  2  (N m -N n )  (  o -  ) 1 Fermi’s Golden Rule

  n  m n* mdn* md ~ d  /dq Quantum Mechanics Wave Mechanics Schrödinger Notation Quantum Mechanics Matrix Mechanics Dirac Notation Classical Analogue Dipole moment change over motion …coordinate q Take Home Message

  n  m n* mdn* md ~ d  /dq Quantum Mechanics Wave Mechanics Schrödinger Notation Quantum Mechanics Matrix Mechanics Dirac Notation Classical Analogue Dipole moment change over motion …coordinate q Take Home Message  ~

 = (4  /3ħc)  n  e  m  2  (N m -N n )  (  o -  ) Square of the transition moment  n  e  m  2 2.Frequency of the light  3.Population difference (N m - N n ) 4.Resonance factor - Dirac delta function  (0) = 1

ABC Rotation of a Diatomic Molecule

For pure rotational transitions a molecule must have a permanent dipole moment

Observing the dipole change from the side i.e. the direction of propagation

dμ/dθ ≠ 0

Selection Rules Harry Kroto 2004 ∆N = ?

(N m - N n ) N m -N m

N m = N o e -∆E/kT In the case of degenerate levels such as rotational levels eacj J level is 2J+1 degenerate we get N m = N o e-∆E/kT J 2J+1 e -∆E/kT N m /N o F(J)

J 2B 4B 6B 8B 10B 12B 14B 16B0 Boltzmann

pedia.org/wi ki/Boltzmann _constant Boltzmann

N m = N o e -∆E/kT In the case of degenerate levels such as rotational levels eacj J level is 2J+1 degenerate we get N m = N o e-∆E/kT J 2J+1 e -∆E/kT N m /N o F(J)

J 2B 4B 6B 8B 10B 12B 14B 16B0 Boltzmann

Boltzmann Population with Degeneracy

N m = N o e -∆E/kT In the case of degenerate levels such as rotational levels each J level is 2J+1 degenerate we get N m = N o (2J+1)e -∆E/kT J 2J+1 e -∆E/kT N m /N o F(J)

J 2B 4B 6B 8B 10B 12B 14B 16B0 Boltzmann

C≡O

CO Rotational Spectrum PROBLEM

Separation Vibration Rotation

ABC H Atom

H Atom Spectrum A

Positronium - +

Einstein Coefficients nn mm

Harry Kroto 2004 H 21 cm Line