7/27/2019 Absorption and Transmission of Light
1/12
Absorption and Transmission of lightand the Beer-Lambert Law
Lecture 21
www.physics.uoguelph.ca/~pgarrett/Teaching.html
7/27/2019 Absorption and Transmission of Light
2/12
Review of L-20
Ring wave functions (circumference )
Energy levels
( )=
nx
xns
2
sin
2
,
( )=
nxxnc
2cos
2,
n =1,2,3,
10, =c ( n =0 )
2
22
2 en
m
hnE =
7/27/2019 Absorption and Transmission of Light
3/12
Review of L-20
Energy levels in a ring molecule
2
2
2 em
h
2
2
2
4
em
h
2
2
2
9
em
h
2
2
2
16
em
h
2
2
2
25
em
h
sin solution cos solutionn = 0
n = 1n = 2
n = 3
n = 4
n = 5
7/27/2019 Absorption and Transmission of Light
4/12
Consider a beam of light on a material
It can be scattered, absorbed, or transmitted
Transmitted light
Light emerges propagating in the same direction as the incident light
Absorbed light Energy from light is absorbed in the volume of the material
Scattered light
Light emerges in a different direction from the incident light
Absorption and Transmission
transmitted
scattered
absorbedincident light
7/27/2019 Absorption and Transmission of Light
5/12
Absorption and Transmission
Absorption and scattering take place at the molecular and
atomic level
For energy from light to be absorbed, it must match available energy
states in the atoms or molecules, or it can scatter from the molecule,
atom, or electrons, (like billiard balls)
ex. Promotion of an e to
an excited state
7/27/2019 Absorption and Transmission of Light
6/12
Cross sections
Light incident upon a material may or may notbe removed
from the incident beam
Probability that the light is removed from the incident beamis related to the cross section
Cross section is like an effective area of the atom or molecule
can be larger or smaller than the geometric cross section
takes into account the absorption and scattering of light
B2 Stealth bomber of the
US has a radar cross
section smaller than that
of hummingbird
7/27/2019 Absorption and Transmission of Light
7/12
Beer-Lambert Law
Consider light incident on a material with areaA andthickness dx and concentration of molecules C( i.e. #/cm3 )
Number of molecules illuminated by light of incidentintensityIx is CAdx
Total effective area that the molecules present is CAdx
Probability of light being absorbed or scattered out of the
beam in thickness dx is
where dIx is the change inintensity across dx
areaA
thickness dx
intensityIx
dxA
CA
I
dI
x
x =
7/27/2019 Absorption and Transmission of Light
8/12
Beer-Lambert Law
We have
Now integrate both sides
The coefficient =Cis the linear attenuation coefficient If we ignore scattering, we can equate the linear attenuation
coefficient with the linear absorption coefficient
dxA
CA
I
dI
x
x =
( ) ( )
xCx
xI
Ix
x
eIeII
CxIIII
CdxI
dI
00
0
0
0
lnlnln
0
==
==
=
7/27/2019 Absorption and Transmission of Light
9/12
Beer-Lambert Law
The Beer-Lambert Law
The intensity of light decreases exponentially with depth in
the material
Linear attenuation coefficient usually expressed in units ofcm1
is a function of wavelength =()
So Beer-Lambert Law is also a function of, i.e.
xCxeIeII 00 ==
xeII
)(
0 )()(
=
7/27/2019 Absorption and Transmission of Light
10/12
Transmittance
Transmittance is defined as
A quantity called absorbance A is defined as
This definition includes both absorption and scattering
A further definition is the extinction coefficient
so
)(
)(
0
I
IT=
( )
( ) xexA
eeI
I
I
IA
x
x
4343.0log
log)(
)(log
)(
)(log
0
00
==
===
4343.0=
CxA =
7/27/2019 Absorption and Transmission of Light
11/12
Absorbance and the extinction coefficient
Absorbance is useful since it can be summed for layers of
different materials, each with their ownx, C, , etc.
A specialized device to measure the intensity of light as a
function of wavelength is the spectrophotometer
Come in various varieties absorption, fluorescence,
++=
+++=
222111
321
xCxCA
AAAA
tot
tot
light source monochromator sample detector
tungsten lamp
produces white
light +UV+IR
diffraction grating
extracts a very narrow
wavelength band
measures light intensity
compared to light incident
on sampleinterchangeable
7/27/2019 Absorption and Transmission of Light
12/12
Absorption spectrum
Absorption spectra for chlorophyll