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