Transcript Light
Light
Photons
• The photon is the gauge boson
of the electromagnetic force.
– Massless
– Stable
– Interacts with charged
particles.
• Photon velocity depends on the
medium.
– c = 2.99792458 108 m/s
– n = index of refraction
c c n
• The light year is a distance, 1 ly
= 9.5 1012 km.
Measuring Photons
• Photons can act as waves or
particles.
• Wavelength () and frequency
(n) are associated with waves.
– Preferred for low energy
photons
• Energy is associated with
particles.
– Preferred for high energy
photons in units of eV
n c
E hn hc
hc = 1.240 keV nm
Electromagnetic Radiation
• Traditional upper boundaries for types of EM radiation:
(m)
n (Hz)
E (eV)
Radio waves
1
3108
1.2410-6
Microwaves
110-3
31011
1.2410-3
Infrared
0.7510-6
41014
1.65
Visible light
0.410-6
7.51014
3.1
Ultraviolet light 1.210-8
2.41016
1102
X-rays
1.410-11
31019
1.2105
Gamma rays
(highest energy)
Sources of Photons
• Accelerated charges emit photons.
– Continuous or discrete spectra may result
Emitted photon
Moving charge
• Photons can be reabsorbed as well.
Kirchhoff’s Radiation
• Radiated electromagnetic
energy is the source of
radiated thermal energy.
– Depends on wavelength
• Objects can emit and absorb
electromagnetic energy.
– Emission coefficient e
– Absorption coefficient a
• Expect a distribution I that
depends on temperature.
e
I
a
Black Body
• A black object is perfectly
absorbing.
– Absorption coefficient is 1
• The distribution is just due to
emission.
I e
• An isolated cavity with a
narrow hole radiates like a
perfectly black body at the
same temperature (1859).
Blackbody Thermodynamics
U 3 pV
U (T ,V ) Vu(T )
V W (n , T )dn
• Assume the cavity has particles
which interact with the wall.
– Relativistic photon energy
– Relate to energy density
0
dU
dp
p T
dV T
dT V
du
u
4
dT
T
u (T ) u0T 4
• Apply the 2nd law to the energy.
– Stefan-Boltzmann law
• Real objects have a factor for
emissivity e.
Quantized Blackbody
2c 2 h
W ( , T ) 5 hc / kT
e
1
For large E=hn
W ( , T )
max T
2c 2 h
5
e hn / kT
hc k
2.9 10 3 m K
4.9651
2k 4 4
4
Wtot (T )
T
T
15c 2 h 3
• The power spectrum is defined
by the power per unit area per
unit wavelength.
– Differential spectrum
– W/m3 or Wcm-1 mm-1
• The integral is the StefanBoltzmann law.
5.67 10 8 W/m 2 K 4
Blackbody Radiation
• Heated gas radiates
electromagnetic energy as
blackbody radiation.
• The frequency spectrum power
is a function of temperature.
– W(,T)
intensity
low
energy
high
energy
• Earth surface: 300 K 20 ºC
• Sun surface: 5800 K 6100 ºC
• Sun interior: 1.57107 K
frequency
Atoms and Light
• Atomic electron energy levels are a source of discrete
photon energies.
• Change from a high to low energy state produces a photon.
• Atoms can also absorb a photon to excite an electron.
Hydrogen
• Hydrogen is the most common
element.
n=3
n=2
• Emission series for hydrogen
have defined names for inner n.
– Lyman 1
– Balmer 2
– Paschen 3
n=1
2
En ( H )
1 me e 4
2 2
4
e
2
n
0
Discrete Spectrum
• Each atom has its own set of energy levels.
• Each atom generates photons at specific frequencies.
• The pattern of frequencies identifies the atom.
helium
neon
Absorption Lines
• Ionized gases at a star’s surface absorb specific
frequencies of light.
• These appear as dark lines in a star’s spectrum.
• Since gases ionize at different temperatures, the
appearance of lines indicate the temperature of the star.
Molecular Spectra
• Energy states in molecules
contribute to stellar spectra.
• Internuclear distances are
quantized in discrete states.
– Vibrational energy
• Angular momentum for the
molecule is quantized.
– Rotational energy
Fluorescence
10-12 s
• Atoms and molecules can
reemit absorbed energy.
S1
10-15 s
S0
10-7 s
• Fluorescence typically involves
three steps.
– Excitation to higher energy
state.
– Loss of energy through
change in vibrational state
– Emission of fluorescent
photon.
X-Rays
• X-rays are associated with
energetic transitions in atoms.
• Continuous spectra result from
electron bombardment.
• Discrete spectra result from
electron transitions with an
atom.
electrons
target
x-ray
Bremsstrahlung
• Acceleration of a charged
particle is associated with a
photon.
– Bremsstrahlung means
braking radiation
– Electrons passing through
matter
– Continuous spectrum x-rays
g
e
e
Z
Photoelectric Effect
• A photon can eject an electron
from an atom.
– Photon is absorbed
– Minimum energy needed
for interaction.
– Cross section decreases at
high energy
g
e
Z
K e hn
Compton Effect
• Photons scattering from atomic
electrons are described by the
Compton effect.
– Conservation of energy and
momentum
g’
g
q
f
e
hn mc2 hn E
hn hn
cos q P cos f
c
c
hn
sin q P sin f
c
hn
hn
1
hn
(1 cos q )
2
mc
Compton Energy
• The frequency shift is
independent of energy.
• The energy of the photon
depends on the angle.
– Max at 180°
• Recoil angle for electron related
to photon energy transfer
– Small q cot large
– Recoil near 90°
h
(1 cos q )
mc
K
cot
q
hn (1 cos q )
mc2 / hn 1 cos q
hn
1 2 tan f
2 mc
Gamma Rays
• Gamma rays are photons associated with
nuclear or particle processes.
– Energy range overlaps: soft gamma
equals hard x-ray
• Nuclear gamma emissions are between
isomers.
– A and Z stay constant
– Distinct energies for transitions
Nuclear Radiation
• Nuclear decay can leave a
nucleus in an excited state.
– Many possible states may
be reached
– Lifetime typically 10-10 s
• Excess energy may be lost as a
photon or electron.
– Single gamma
– Series of gamma emissions
– Internal conversion beta
226
88
Ra
4.785 MeV
94.4%
a
222
86
Rn
5.5%
a
2.2%
0.186 MeV
3.3% b
0 MeV