Download 6.1 Electromagnetic Waves

6.1 Electromagnetic Waves
• electromagnetic radiation can be described as
a harmonic wave in either time or distance
• waves are characterized by their period,
frequency, wavelength and wave number
• Planck's Law gives the energy of
electromagnetic quanta
• ν and λ are related by the speed of light,
which in turn is determined by the refractive
index
• electromagnetic radiation is characterized by
both an electric field and magnetic field
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Temporal Harmonic Wave
1
t0
0.5
amplitude (V/m)
An electromagnetic wave can be
described in either __________
__________. When amplitude is
measured as the wave passes a
fixed location the result is a
temporal wave.
0
-1
The wave is given by
0
1
2
-0.5
-1
time (fs)
where t0 is the period. Usually the expression is written using
frequency, where ν = 1/t0. ν has units of ___________. In
some cases it is convenient to use angular frequency, ω = 2πν. ω
also has units of ____ (which may be called radians per second).
E = E0 cos ( 2πν t )
E = E0 cos (ωt )
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3
Spatial Harmonic Wave
The wave is given by
1
λ
0.5
amplitude (V/m)
When a "snapshot" of the wave is
taken, the wave will extend over
distance in the laboratory.
0
-300
0
300
600
-0.5
where λ is the wavelength. In the
visible λ has units of ____, in the
infrared units of _______.
-1
distance (nm)
Sometimes the expression is written using wave number, ν = 1 λ
ν has units of reciprocal centimeters (cm-1). In physical optics it
is convenient to use the k-vector, k = 2π/λ. The units of k are
usually reciprocal meters (m-1).
E = E0 cos ( 2πν x )
E = E0 cos ( kx )
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900
Plane, Spherical and Cylindrical Waves
• a three dimensional plane wave is given by
(
)
E = E x cos ( k x x ) + E y cos k y y + E z cos ( k z z )
• a spherical wave is given by
• a cylindrical wave is given by
E=
E0
cos ( kr )
r
E=
E0
kr
cos ( kr )
r
z
plane wave
6.1 : 4/11
spherical wave
Energy per Quantum
The energy per quantum is given by Planck's Law,
E = hν =
hc
λ
= hcν
where h = 6.6×10-34 J s. Note that E is proportional to ν and ν ,
but not λ!
The concept of a quantum is only relevant when the energy
delivered is above the thermodynamic noise given by 4kT, where
k = 5.6×10-23 J K-1. At room temperature this limit is given
approximately by,
ν=
4kT
= 2.5 × 1013
h
Hz
which is ____________________.
For a bond energy of 400 kJ mol-1, the bond energy per molecule
is 6.6×10-19 J. This is delivered by one quantum of 1015 Hz (300
nm) radiation. All higher frequencies are considered _________.
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Refractive Index
For electromagnetic radiation, frequency and wavelength are
related by the speed of light, c = 3×108 m s-1.
When electromagnetic radiation travels through material with
polarizable electrons, it slows down. Because the quantum of
energy remains fixed, the frequency remains fixed. This means
that the wavelength decreases.
The refractive index is given by the ratio of velocities, ________.
6.1 : 6/11
substance
n589
substance
n589
perfluorohexane
water
ethanol
1.25
1.33
1.36
quartz
benzene
glass
carbon disulfide
1.46
1.50
1.52
1.63
Dispersion
The refractive index depends upon the wavelength, ordinarily
_________ from the violet toward the red. The change in value
is called dispersion.
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1.75
flint glass
1.625
refractive index
Shown at the right
are dispersion
curves for three
materials used to
make prisms.
Dispersion is
greatest near an
______________
______________.
Quartz is a good
prism material for
the UV, while flint
glass is good for
the visible and
near IR.
crown glass
1.5
quartz
1.375
1.25
200
400
600
800
wavelength (nm)
1000
1200
Propagation of Light
Maxwell's equations show that a time-varying electric field (E in V
m-1) generates a time varying magnetic field (H in A m-1), and
that a time varying magnetic field generates a time varying
electric field. Thus, electromagnetic radiation is ____________.
When E is aligned in the x-direction and the wave is traveling in
the z-direction, the generated magnetic field is in the y-direction.
E = E x cos ( 2π z / λ )
H = H y cos ( 2π z / λ )
In a vacuum the ratio of Ex and Hy are given by the impedance of
free space.
Ex
1
=
=
H y ε 0c
Note that the two waves are in phase and that the direction of
propagation is given by E×H. The radiant flux density transmitted
in the z-direction is given by ExHy in units of W m-2. When
intensity is used the flux is given by photons s-1 m-2.
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Electromagnetic Spectrum
frequency (Hz)
1019
gamma rays
1017
1015
ultraviolet
x-rays
10-10
1013
infrared
10-6
wavelength (m)
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109
radio
visible
10 -8
10 11
microwaves
10-4
10-2
100
Spectral Regions and Phenomena (1)
• radio waves: below 1 GHz, natural units Hz
P nuclear magnetic resonance, used to determine bonding
in molecules
P electron spin resonance, used to determine location of
unpaired electrons
• microwaves: 1 GHz to 1 THz, natural units Hz or cm-1
P ___________________, used to determine bond angles
and lengths of small molecules in the gas phase
• infrared (below red): 10,000 cm-1 to 50 cm-1, natural units cm-1
or μm
P ___________________ of molecules, used to determine
functional groups existing within a molecule
• visible: 400 nm to 750 nm, natural units nm or cm-1
P valence shell electronic transitions, used to identify atoms
in a sample and concentration
P molecular electronic transitions involving __________
________________, used to determine structure and
concentration
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Spectral Regions and Phenomena (2)
• ultraviolet (beyond violet): 10 nm to 380 nm, natural units nm
or D
P valence shell _________________________, used to
identify atoms in a sample and their concentration
P molecular electronic transitions involving single bonds,
used to determine structure and concentration
• x-rays: 0.1 D to 100 D , natural units D
P _______________________________, used to identify
atoms in solids and provide information about adjacent
bonded atoms
• gamma rays: greater than 0.1 MeV, natural units electron volts
(1 eV = 1.6×10-19 J)
P ______________________, used to identify isotopes
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