Separation of Motion QM. Separation Vibration Rotation.

Separation of Motion QM

Separation Vibration Rotation

= (4/3ħc) n em2 (Nm-Nn) (o-)

1 2 3 4

1. Square of the transition moment n

em2

2. Frequency of the light

3. Population difference (Nm- Nn)

4. Resonance factor - Dirac delta function (0) = 1

= (4/3ħc) n em2 (Nm-Nn) (o-)

1

Fermi’s Golden Rule

Dipole Moment Matrix Elements

= (4/3ħc) n em2 (Nm-Nn) (o-)

1

Fermi’s Golden Rule

μ = q.r

+ -r

Dipole Moments

CO2 Vibrations

Einstein Coefficients

n

m

= (4/3ħc) n em2 (Nm-Nn) (o-)

1 2 3 4

1. Square of the transition moment n

em2

2. Frequency of the light

3. Population difference (Nm- Nn)

4. Resonance factor - Dirac delta function (0) = 1

Frequency

●-----●

Problem 3

Devise a simple experiment using fairly everyday things to estimate

the frequency of a light source

…or alternatively devise an experiment to determine the

wavelength and assume

c = 30000kms-1

= (4/3ħc) n em2 (Nm-Nn) (o-)

1 2 3 4

1. Square of the transition moment n

em2

2. Frequency of the light

3. Population difference (Nm- Nn)

4. Resonance factor - Dirac delta function (0) = 1

http://en.wikipedia.org/wiki/Boltzmann_constant

Boltzmann

n

m

o

Nm = No e -∆E/kT

where

∆E = Em – Eo

n

m

o

Nm = No e -∆E/kT

where

∆E = Em – Eo

Maser

= (4/3ħc) n em2 (Nm-Nn) (o-)

1 2 3 4

1. Square of the transition moment n

em2

2. Frequency of the light

3. Population difference (Nm- Nn)

4. Resonance factor - Dirac delta function (0) = 1

Dirac delta function

δ(0)

1. Infinitely high

2. Infinitely narrow

3. Area = unity

Resonancecommons.wikimedia.org

Millennium Bridge

Tacoma

ABC Rotation of a Diatomic Molecule