CHAPTER 14 OPTICAL SPECTROSCOPY 299

We can then write:

(db14.4)

This term has the advantage that it can be related directly to the experimental measured
absorption band:

(db14.5)

This relation can be derived using the Beer–Lambert law:

(db14.6)

This can be rewritten as:

(db14.7)

In these equations σis the absorption cross-section and is associated with each molecule in
the sample. To change the units to moles per liter we introduce Avogadro’s number NAand
can write:

(db14.8)

and

ε=σNA 10 −^3 loge (db14.9)

This gives:

(db14.10)

These values are specific frequencies, so to obtain the total values we integrate:

B (db14.11)

c

hN e

D

Alog

==∫

10

6

3

0

2

ε

υ

υ

ε

d

3

Z

NB

NI z

Ne

B

c

A hN

ρ

ε

υ

ε

log NeAlog υ

==

10

10

(^3) d 3 1
or witth ρ
υ

h
c

I

log ( log )ln log

I

I

Ae

I

I

(^0) Nl e lc
0
==− =σε=
d
d

′

′

∫∫=−

I

I

Nz
I

Il

0 0

σ

Nz

I

I

d

d

=−

′

′

1

σ

D

hc

(^3) eNA

()

log

()

= ∫

10 3

8

3

π^3

ευ

υ

dυ

B

D

=

3

6 ε 0 Z^2