Physics 2D Lecture Slides Oct 21 Vivek Sharma UCSD Physics
Modern View of Photoelectric Effect = = + ϕ E hf KE
Is “h” same in Photoelectric Effect as in BBQ Radiation? Slope h = 6.626 x 10 -34 JS Einstein � Nobel Prize! No matter where you travel in this galaxy and beyond… h = Planck’s constant is the SAME !!! NOBEL PRIZE FOR Herr PLANCK
Work Function (Binding Energy) In Metals
Photoelectric Effect on An Iron Surfa ce: µ 2 2 Light of Intensity I = 1.0 W/cm inc ident on 1.0cm surfa ce of F e A ssume Fe reflects 96% of ligh t λ further on ly 3% of incident li ght i s V i olet region ( = 250nm) barely above thres hold frequency for Ph . El effec t × × µ 2 (a) Intensity available for Ph. El eff ect I =3 % 4% (1.0 W/c m ) (b) how m any photo-electrons e mitted per s econd ? × × µ λ 2 Power 3% 4 % (1.0 W/c m ) = # of p hoto electro n s = h f hc × − × − 9 9 (250 10 m )(1.2 10 J / ) s = 8 − × × 34 (6.6 10 J s i )(3.0 1 0 m s / ) × 9 = 1.5 10 × × = × − -19 9 10 (c) Current in Ammeter : i = (1.6 10 C )(1.5 10 ) 2.4 10 A − Φ = × × -15 15 1 (d) Work Function = h f ( 4.14 1 0 eV s i )( 1.1 10 s ) 0 = 4.5 eV
Photon & Relativity: Wave or a Particle ? • Photon associated with EM waves, travel with speed =c • For light (m =0) : Relativity says E 2 = (pc) 2 + (mc 2 ) 2 • ⇒ E = pc • But Planck tells us : E = hf = h (c/ λ ) • Put them together : hc / λ = pc p = h/ λ – ⇒ – Momentum of the photon (light) is inversely proportional to λ • But we associate λ with waves & p with particles ….what is going on?? –A new paradigm of conversation with the subatomic particles : Quantum Physics
X Rays : “Bremsstrahlung”: Braking Radiation • EM radiation, produced by bombarding a metal target with energetic electrons. • Produced in general by ALL decelerating charged particles X rays : very short λ ≅ 60-100 pm (10 -12 m), large frequency f • • Very penetrating because very energetic E = hf !! Useful for probing structure of sub-atomic Particles (and your teeth)
An X-ray Tube from 20 th Century e Xray The “High Energy Accelerator” of 1900s: produced energetic light : X Ray , gave new optic to subatomic phenomena
X Ray Spectrum in Molybdenum (Mo) • Braking radiation predicted by Maxwell’s eqn • decelerated charged particle will radiate continuously • Spikes in the spectrum are characteristic of the nuclear structure of target material and varies between materials Shown here are the α and β lines for • Molybdenum (Mo) • To measure the wavelength, diffraction grating is too wide, need smaller slits •An atomic crystal lattice as diffraction grating (Bragg)
Interference of Waves: A Reminder = ω + φ Two Identical waves y x t ( , ) y sin( k x - t ) travel along +x and interefere i max i i i ' to give a resulting wave y ( , ). The resulting wave form depends on relative phase differen x t ce 2 ∆ φ π π Read Ch17-8 from Resnick between 2 waves. Shown f o r = 0 , , 3 etal held in Ereserve
Bragg Scattering: Probing Atoms With X-Rays detector X-ray Constructive Interference when net phase difference is 0, 2 π etc This implied path difference traveled by two waves must be integral multiple of wavelength : n λ =2dsin ϑ
Xray picture of a DNA Crystal
Proteins inside Rhinovirus reconstructed by x-ray diffraction
• X rays are EM waves of low wavelength, high frequency (and energy) and demonstrate characteristic features of a wave – Interference – Diffraction • To probe into a structure you need a light source with wavelength much smaller than the features of the object being probed – Good Resolution � λ << ∆ • X rays allows one probe at atomic size (10 -10 )m
Compton Scattering : Quantum Pool ! • 1922: Arthur Compton (USA) proves that X-rays (EM Waves) have particle like properties (acts like photons) – Showed that classical theory failed to explain the scattering effect of • X rays on to free (not bound, barely bound electrons) • Experiment : shine X ray EM waves on to a surface with “almost” free electrons – Watch the scattering of light off electron : measure time + wavelength of scattered X-ray
Compton Effect: what should Happen Classically? • Plane wave [f, λ ] incident on a surface with loosely bound electrons � interaction of E field of EM wave with electron: F = e E • Electron oscillates with f = f incident • Eventually radiates spherical waves with f radiated = f incident – At all scattering angles, ∆ f & ∆λ must be zero • Time delay while the electron gets a “tan” : soaks in radiation
Compton Scattering : Setup & Results ∆ λ = λ − λ ∝ − θ ( ' ) (1 cos ) λ Scattered ' larger than incident ⎛ ⎞ h ∆ λ = − θ (1 cos ) ⎜ ⎟ m c ⎝ ⎠ e How does one explain this startling anisotropy?
Compton Effect : Quantum (Relativistic) Pool
Compton Scattering: Quantum Picture φ = − θ p cos p p 'cos e φ = θ p sin p 'sin e ⇒ Square and add = − θ + 2 2 2 p p 2 pp 'cos p ' e Eliminate p & E using e e 2 = 2 2 + 2 4 E p c m c & e e e = − + 2 E ( E E ') m c e e Energy Conservation: ( ) 2 ⎡ ⎤ − + = − θ + + 2 2 2 2 2 ( E E ') m c p 2 pp 'cos p ' ( m c ) ⎣ ⎦ e e = + 2 E+m c E ' E e e E ⇒ For light p= c Momentum Conserv : θ φ p = p'cos +p cos ⎡ ⎤ 2 2 E E E ' E ' e + − + − = − θ + 2 2 2 2 E E ' 2 EE ' 2( E E ') mc 2 co s c ⎢ ⎥ = θ φ 0 p'sin -p sin 2 2 2 c c c ⎣ ⎦ e Use these to e liminate ⇒ − + − 2 = − θ EE ' ( E E ') mc E E 'cos E-E' 1 h electron deflection ⇒ = − − θ ⇒ λ − λ = − θ (1 cos ) ( ' ) ( )(1 co s ) 2 EE' m c m c angle (n ot measured ) e e
Checking for h in Compton Scattering Plot scattered photon data, calculate slope and measure h It’s the same h !! c m e / h = λ C ∆λ h h λ − λ = − θ ( ' ) ( )(1 cos ) t g n m c e l e e v a w n o t Energy Quantization is a p m o UNIVERSAL characteristic C of light (EM Waves) 1-cos ϑ
Blindmen & an Elephant touched the trunk of the elephant, said elephant was like a branch of a tree . touched the tail of the elephant, said elephant was like a snake. touched an ear. He said elephant was a huge fan. felt a leg of the elephant., elephant was like a pillar . touched the side of the elephant, said the elephant was like a wall Gentlemen, all five of you have touched only one part of the elephant ..elephant is all of above LIKEWISE WITH LIGHT !
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