Chapter 2 Particle properties of waves

Transcription

1 Chapter Partile properties of waves Eletronis: partiles Eletromagneti wave: wave harge, mass Wave? diffration, interferene, Polarization partile?.1emwaves Wave-partile Duality Changing magneti field urrent (or voltage) Maxwell proposed: hanging eletri field magneti field Hertz reated EM waves and determined the wavelength and speed of the wave, and showed that they both have E and B omponent, and that they ould be refleted, refrated, and diffrated. Wave harateristi. 1

2 Priniple of Superposition: When two or more waves of the same nature travel past a point at the same time, the instantaneous amplitude is the sum of the instantaneous amplitude of the individual waves.

3 Construtive interferene Destrutive interferene same phase, greater amplitude different phase, partial or ompletely anellation of waves Interferene wave harateristi Young s diffration experiments: diffration wave harateristi 3

4 .Blakbody radiation Is light only onsistent of waves? Amiss: understand the origin of the radiation emitted by bodies of matter. Blakbody: a body that absorbs all radiation inident upon it, regardless of frequeny. A blakbody radiates more when it is hot than it is old, and the spetrum of a hot blakbody has its peak at a higher frequeny than that of a ooler one. 4

5 Considering the radiation inside a avity of absolute temperature T whose walls are perfet refletors to be a series standing EM waves. L n* / Density of standing waves in avity G 3 ( ) d 8 d / The higher ν, the shorter the wavelength, and the greater the number of possible standing waves. The average energy per degree of freedom of an entity that is a member of a system of suh entities in thermal equilibrium at T is 1/kT. K is Boltzmann s onstant=1.381*10-3 J/k 5

6 An idea gas moleular has three degree of freedom: kineti energy in three independent diretions 3/kT One dimensional harmoni osillator has two degree of freedom: kineti energy and potential energy. Eah standing wave in a avity originates in an osillating eletri harge in the avity wall. Two degree of freedom. Classi average energy per standing wave kt Total energy per unit volume in the avity in and +d u ( ) d G( ) d (8 kt/ 3 ) d Rayleigh-Jeans formula inrease energy density inrease with. In the limit of infinitely high frequenies, u( )d goes to infinity. In reality, the energy density(and the radiation rate)falls to 0 as goes to infinity. Ultraviolet atastrophe 6

7 Plank Radiation Formula u( )d =(8πh/ 3 )( 3 d )/(e h /kt -1) h is plank s onstant=6.66*10-34 Js h >>kt e h /kt u( ) 0 No ultraviolet atastrophe. In general, e x =1+x+x /+ When h << kt, 1/(e h /kt -1)~1/((1+(h /kt)-1)~kt/h u( )d ~(8πh/ 3 )( 3 d )/( kt/h )~(8πkT/ 3 ) d whih is Rayleigh-Jeans formula. 7

8 How to justify the Plank radiation formula The osillators in the avity walls ould not have a ontinuous Distribution of possible energy ε but must have only speifi energies ε n =nh n=0,1, An oillator emits radiation of frequeny when it drops from one energy state to the next lower one, and it jumpsto the next higher state when it absorbs radiation of. Eah disrete bundle of energy h is alled a quantum. With osillator energies limited to nh, the average energy per osillator in the avity walls turn out to be not kt as for a ontinuous distribution of osillator energies, but ε=h /(e h /kt -1) average energy per standing wave 8

9 .3 Photoeletri effet Some of photoeletrons that emerge from the metal surfae have enough energy to reah the athode despite its negative polarity Current When V is inreased to a ertain value V 0, no more photoeletrons arrive. V 0 orrespond to the max photoeletron kineti energy. Three experimental finding: (1) No delay between the arrival of the light at the metal surfae and the emission of photoeletrons. () A bright light yields more photoeletrons than a dim one, but highest eletron energy remain the same. 9

10 (3) The higher the frequeny of the light, the more energy the photoeletrons have. At the frequenies smaller than 0, whih is a harateristi of the speifi metal, no more eletrons are emitted. Quantum theory of light Einstein proposed Photons. The energy in light is not spread out, but is onentrated in small pakets. Eah photon of light of frequeny has the energy h. Einstein proposed that energy was not only given to em waves in separate quanta but was also arried by the waves in separate quanta. 10

11 Explanation of experiments: (1) Sine em wave energy is onentrated in photons and not spread out, there should be no delay in the emission. () All photons of frequeny have the same energy h. Changing the intensity of light only hange the number of photoeletrons but not their energy. (3) The higher, the greater photon energy and so the more energy the photoeletrons have. ν o orresponds to the min energy Φ for the eletron to esape from the metal surfae. This energy is alled work funtion. Φ=hν o Photoeletri effet hν=ke max +Φ h = ke max +hν o ke max =h(ν-ν o ). Photo energy E=(6.66*10-34 Js/1.60*10-19 J/eV )ν=(4.136*10-15 )νevs ν=/λ E=1.4*10-6 evm/λ 11

12 What is light Wave model: light intensity E Partile model: light intensity N(#of photons/se.area) N E.N is large interferene pattern N is small a series of random flashes.if keep trak of flashes for long time same as large N intensity of wave at a given plae on the speifi spae the probability of finding photons. 1

13 Wave & quantum theory omplement eah other. photoeletri effet : E photons E e yes faster e x-ray more x-ray # of e inrease Intensity of x-ray inrease.for given aelerating V λ min V.most of e λ min heat A few e lose E in single ollisions x-ray 13

14 .x-ray are em waves EM theory predits that an aelerated eletri harge will radiate em waves, and a rapidly moving e suddenly brought to rest is ertainly aelerated Bremsstranlung ( braking radiation ) x-ray at speifi λ nonlassial * different targets give different harateristi x-ray * for the same V, λ min is the same for different materials λ min =( )/V(m) 14

15 hν max = Ve = h/λ min λ min = h/ve = ( )/V Sattering by an atom (wave model) atom in E polarized distorted harge distribution eletri dipole em wave with ν on atom polarization harge with ν osillating eletri dipole radiate em wave x-ray falls on a rystal will be sattered in all diretions beause of regular arrangement of atoms onstrutively interferene Bragg s ondition (dsinθ=λ) 15

16 Compton effet Loss in photon energy=gain in e energy hν -hν =ke for massless partile E= P (P=momentum) photon momentum P =E/ = hν/ 16

17 hν/ = (hν /)osφ+ Posθ (parallel)..(1) 0 = (hν /)sinφ Psinθ ().() (1)&()x P(osθ) = hν -hν osφ P(sinθ) = (hν )sinφ P = (hν) (hν)(hν )osφ +(hν ) 17

18 & E = KE + m o 4 E = m o P (KE + m o ) = m o 4 + P P = KE + m o KE Beause KE = hν - hν P = (hν - hν ) + m o KE m o (hν - hν ) = (hν)(hν ) (1 osφ) (3) (3)/h m o /h(ν/ - ν /) =(ν/)( ν /)(1 osφ) m o /h(1/λ 1/λ ) =(1 osφ)/( λλ ) λ - λ = (h/m o )(1 osφ) = λ(1 osφ) λ=compton wavelength 18

19 Relativisti formulas Total energy E= m o v 1 m o = rest mass Relativisti momentum P = m o v 1 v When m o = 0 (massless partile) & v< E=P=0 How about v=, m o = 0 E=0/0, P=0/0 (any values) E = 4 m o 1 v, P = m o v v 1 P = m o v v 1 E P = 4 m o 1 v (1-v / ) = m o 4 E = m o 4 +P 4 For all partiles E= p m = E o p 0 Restrition of massless partiles : E = P (m o =0) Total energy m =m o +KE = m o 1 v 19

20 Pair prodution A photon give an e all of its energy part of its energy photoeletri ompton a photon materialize into an e & position 0

21 (momentum is onserved with the help of the nuleus whih arries away enough photon momentum) rest energy m o of eletron or position is 0.51Mev pair prodution requires a photon energy 1.0Mev pair prodution annot our in empty spae onervation of energy hν = m momentum onervation hν/ = Posθ hν = P(osθ) P = mv hν = m (v/) osθ v/ <1 & osθ 1 hν < m 1

22 linear attenuation oeffiient di I udx I = I o exp(-ux) absolute thikness x = ln( I o ) I u