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

• The light year is a distance, 1 ly = 9.5 1012 km.

ncc

Measuring Photons

• Photons can act as waves or particles.

• Wavelength () and frequency () are associated with waves.

– Preferred for low energy photons

• Energy is associated with particles.

– Preferred for high energy photons in units of eV hc = 1.240 keV nm

c

chhE

Electromagnetic Radiation

• Traditional upper boundaries for types of EM radiation:

(m) (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

Moving charge

Emitted photon

• 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 – Absorption coefficient

• Expect a distribution I that depends on temperature.

I

• A black object is perfectly absorbing.

– Absorption coefficient is 1

• The distribution is just due to emission.

• An isolated cavity with a narrow hole radiates like a perfectly black body at the same temperature (1859).

Black Body

I

Blackbody Thermodynamics

• Assume the cavity has particles which interact with the wall.

– Relativistic photon energy

– Relate to energy density

• Apply the 2nd law to the energy.

– Stefan-Boltzmann law

• Real objects have a factor for emissivity .

40)( TuTu

pVU 3

0),(

)(),(

dTWV

TVuVTU

VT dT

dpTp

dV

dU

T

u

dT

du4

Quantized Blackbody

• The power spectrum is defined by the power per unit area per unit wavelength.

– Differential spectrum

– W/m3 or Wcm-1 m-1

• The integral is the Stefan-Boltzmann law.

12

),(/5

2

kThce

hcTW

kThehc

TW /5

22),(

For large E=h

4432

4

15

2)( TT

hc

kTWtot

Km109.29651.4

3max

khcT

428 KW/m1067.5

low energy

high energy

frequency

intensity

Blackbody Radiation

• Heated gas radiates electromagnetic energy as blackbody radiation.

• The frequency spectrum power is a function of temperature.

– W(,T)

• Earth surface: 300 K 20 ºC

• Sun surface: 5800 K 6100 ºC

• Sun interior: 1.57107 K

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.

• Emission series for hydrogen have defined names for inner n.

– Lyman 1

– Balmer 2

– Paschen 3n = 1

n = 2

n = 3

22

42

0)( 24

1

n

emE e

Hn

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

• Atoms and molecules can reemit absorbed energy.

• Fluorescence typically involves three steps.

– Excitation to higher energy state.

– Loss of energy through change in vibrational state

– Emission of fluorescent photon.

10-15 s

S1

S0

10-12 s

10-7 s

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.

target

electrons

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

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

e

Z

hKe

Compton Effect

• Photons scattering from atomic electrons are described by the Compton effect.

– Conservation of energy and momentum

e

’

Ehmch 2

coscos P

c

h

c

h

sinsin P

c

h

)cos1(1 2

mch

hh

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 cot large

– Recoil near 90°

)cos1( mc

h

cos1/

)cos1(2

hmc

hK

tan1

2cot

2

mc

h

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

4.785 MeV

Rn22286

0.186 MeV

0 MeV

94.4%

5.5%

2.2% 3.3%

Ra22688