LightWe can use different terms to describe light:

• Color

• Wavelength

• Frequency

Light is composed of electromagnetic waves that

travel through some medium.

LightThe properties of the medium determine how light

travels through it.

In a vacuum, light waves travel at a speed of 3.00

x 108 m/s or 186,000 miles/s.

The speed of light in a vacuum is a constant that

is tremendously important in nature and

science—it is given the symbol, c.

Because light behaves like a wave, we candescribe it in one of two ways—by itswavelength or by its frequency.

= wavelength—distance between two adjacent wavecrests. has units of distance—frequently nanometers(nm).

= frequency—how many times the wave goes up anddown in a period of time. has units of inverse time(s-1 Hz[hertz]).

Light (con’t.)

Light (con’t.)

If you know either the frequency or thewavelength, you can calculate the other quantitythrough the relationship:

c = •

c = speed of light (3.00 x 108 m/s)

= wavelength (m)

= frequency (s-1)

A “particle” of light is called a photon.

ExamplesDiode laser pointer: = 670 nm

670 nm = 670 x 10-9 m

Photon with frequency: = 4.3 x 1013 Hz

nm 6980 m 6.98 m 10 x 6.98

s 10 x 4.3

s m 10 x 3.00

c

6-

1-13

1-8

=μ====

Light (con’t.)The type of light (ultraviolet, visible, infrared, x-ray,

etc.) is defined by either its frequency or

wavelength:

103 m

102 Hz

wavelength

frequency

gamma rays x-rays ultraviolet infrared microwave radio waves

10-5 nm 10-3 nm 1 nm 400

nm

700

nm

103 nm 106 nm 1 m

1024 Hz 1016 Hz 1012 Hz 1010 Hz 108 Hz 106 Hz 104 Hz1022 Hz 1020 Hz 1018 Hz visible

light

7 x 1014 Hz 4 x 1014 Hz

Light (con’t.)

The energy of light can be determined either from

its wavelength or frequency:

== h E or c h

E

Planck’s constant: h = 6.626 x 10-34 J s

Examples

4.3 x 1013 Hz ( ) light (6980 nm = 6.98 μm):

E = (6.626 x 10-34 J s)(4.3 x 1013 s-1) = 2.85 x 10-20 J

= 17.2 kJ mol-1

670 nm ( ) diode laser:

E = (6.626 x 10-34 J s)(3.00 x 108 m s-1) = 2.97 x 10-19 J

(670 x 10-9 m)

= 179 kJ mol-1

Examples (con’t.)

Violet light from a mercury lamp has a wavelength

of 436 nm:

E = (6.626 x 10-34 J s)(3.00 x 108 m s-1)

(436 x 10-9 m)

= 4.56 x 10-19 J

= 275 kJ mol-1

• Atoms and molecules absorb and emit light inthe ultraviolet (UV), visible (vis), infrared (IR),and microwave (μwave) regions of theelectromagnetic spectrum.

• Absorption or emission of light in the UV and visregions involves movement of electrons in theatom or molecule.• One reason UV light is so damaging is that the light

has enough energy to break chemicalbonds—biological and chemical systems

• E ( = 300 nm) = 399 kJ mol

• Average bond energy = 380 kJ mol-1

Potential Energy Surfaces

Internuclear Distance

1 2 3 4 5 6 7 8 9 10

Re

equilibrium bond length

At large separation, the atoms feel no attractiveforce to each other and represent a brokenchemical bond

As the bond distance decreases, the nuclear repulsioncauses the potential energy to increase dramatically--it requires a lot of energy to hold the positive chargesvery close to each other.

UV/vis Spectroscopy

Transitions in the

UV/visible

portion of the

spectrum

involve

movement of

electrons

between

electronic

energy states:

Distance

1 2 3 4 5 6 7 8 9 10

T1

S0

S1

AbsorptionFluorescence

Phosphorescence

Visible Spectrum of gaseous I2

Wavelength (nm)

500 525 550 575 600 625 6500.0

0.1

0.2

0.3

0.4

0.5

UV/vis Spectroscopy

UV/vis spectroscopy can provide information

about a molecule’s electronic states, its

geometry in the ground state and excited

electronic states, and its ionization potential

UV/vis spectroscopy can also be a powerful

analytical tool to measure concentrations of

atoms and molecules

IR Spectroscopy

Internuclear Distance

1 2 3 4 5 6

v = 0

v = 1

v = 2

v = 3

v = 4

vibrational energy levelsare determined by theirvibrational quantumnumber, v, the geometryof the molecule, and thestrength of the bondsconnecting the atoms

IR transition

Infrared Spectrum of CO2

Frequency (cm-1

)

228023002320234023602380

0.0

0.1

0.2

0.3

0.4

0.5

Infrared Spectrum of C6H6 (benzene)

Frequency (cm-1

)

500100015002000250030003500

0.0

0.2

0.4

0.6

0.8

1.0

x 10

IR Spectroscopy

IR spectroscopy can provide structural

information about a molecule’s geometry and

size and chemical information about which

functional groups the molecule contains

IR spectroscopy can also be used as an

analytical tool to determine concentrations of

species in solution or gas phases

Spectroscopy

Io Ibdx

light source sample cell detector

The intensity of light entering the cell is Io.

Some of the light is absorbed by the sample.

The intensity of light striking the detector is I.

Spectroscopy

Io Ibdx

light source sample cell detector

dx k I- dI =If we look at an infinitesimally

small cross section of the cell,

dx, the change in intensity

across that section is:I is intensity of light entering

that cross sectional area

k is a constant that includes the concentration

of the absorbing species and how strongly it

absorbs light at a specific wavelength

Spectroscopy

dx k- I

dI=

Io Ibdx

light source sample cell detector

Perform separation of variables:

Integrate both sides of

the equality: =b

0

I

I

dx k- I

dI

o

Spectroscopy

b0

II

xk- ln(I)o

=

Io Ibdx

light source sample cell detector

Results of

integration:

Applying limits

of intergration:kb-

I

Iln

o

=

Spectroscopy

exp{-kb} I

Ilnexp

o

=Exponentiate both

side of equality:

After some log

algebra:Cb}exp{- I exp{-kb} I I oo ==

where k = C

= absorption coefficient—a measure of

how strongly the light at a specific

wavelength

C = concentration of absorbing species

Spectroscopy

Cb} - 1{ I I o=

...} CB)(- CB)(- CB)(- {1 I I 32o ++++=

Expand exponential

in a power series:

Truncate series

following linear term:

Rearranging

gives: CB A I

I

o

=I = I-Io

A is the “absorbance”

Spectroscopy

Beer’s Law:

A = Cb

Absorbance is proportional to a species’

absorption coefficient and concentration, and

the path length of light traveling through the

cell

We can also define “transmittance” as:

T = 10-A or A = -log(T)

Optical Spectrometer Design

Light

source

Lens

Monochromator

Data

processing

DetectorSample