absorption and transmission of light

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


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 =


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


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


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


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


7/12

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 =


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

==

==

=


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 )()(

=


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 =


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


12/12

Absorption spectrum

Absorption spectra for chlorophyll

absorption and transmission of light

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