mnmmn NN

mnmmnmn NBN Einstein transition

probability of absorption

TkhTkE

m

n BnmB eeN

N //

nmmnnmnmnnmmmnmnn NNBNBNB

dt

dN

absorptionnetdt

NdNN n

nm 0:

emissionnetdt

NdNN n

nm 0:

mhn

Ground state

n

absorption emission

absorptionneitherdt

NdNN n

nm 0: emissionnor

Inversed Population

kT

1

kTi

i

Aen

iAeni

i

kT

iiegq

BoltzmannDistribution

Calculate the ratio of 1H35Cl (no=2886 cm-1) molecules present in the first vibrtional energy to those in the zeroth level at room temperature and at 1000ºC.

kTi

i

Aen

kTj

j

Aen

kTkT

kT

kT

i

j eee

e

n

n ij

i

j

72981038.1

2886100.3106.6

0

1

0

1

1033.923

1034

en

n

eeen

nkT

hckT

hkT

oo

In this sense, it resembles the wave function in quantum mechanics that contains all information about the quantum system. Partition functions are thus some sort of “thermal wave functions”

The importance of the molecular partition function lies in the fact that it contains all information needed to calculate all macroscopic thermodynamic properties of systems of independent particles

q

eg

eg

egN

TkEi

i

TkEi

TkEi

i

Bi

Bi

Bi /

/

/

Ruby Red

Three-level System

High power consumption

1s2

2p55s1

2p54s1

2p54p1

2p53p1

2p53s1

2p6

1S0

1S0

3S1

collisional transfer

He Ne

Stimulated emission

Electron impact

l=3390 nm

l=632.8 nm

l=1150 nm

radiative

collisional

He-Ne Laser