Final exam: Tuesday, May 11, 7:30-9:30am, Coates 143 Approximately 7 questions/6 problems Approximately 50% material since last test, 50% everyting covered on Exams I-III About 50% of everyting closely based on omeworks One problem will be substantially like one of te problems from Exams I-III Office ours: Monday, May 10, 3-5pm Capter 38: on te web Username: pys10 Passwd: maxwell
Poto(electric)effect 1. For eac material tere is a tresold frequency of ligt: no current at lower frequencies/greater wavelengt.. Once above tis frequency te current depends on te intensity of ligt, below tis frequency it does not. 3. Te stopping voltage depends on te frequency but not intensity of ligt. Pysics (classical): some work required to rip an electron out of metal; ligt is E/M wave, intensity I~ E iger intensity larger electric field greater force everyting sould depend on intensity, not frequency/wavelengt
Poto(electric)effect 1. For eac material tere is a tresold frequency of ligt: no current at lower frequencies/greater wavelengt.. Once above tis frequency te current depends on te intensity of ligt, below tis frequency it does not. 3. Te stopping voltage depends on te frequency but not intensity of ligt. Pysics (new ideas): some work required to rip an electron out of metal; ligt is a collection of particles wose energy depends on frequency iger intensity more of tose particles collisions wit electrons: energy of a ligt particle ( poton ) transferred to an electron minimal frequencyminimal work needed to rip an electron stopping voltagemaximal energy of te electron
Poton wit energy E 0 Electron wit kinetic energy E 0 Φ Material-dependent work function Stopping potential: all kinetic energy went into potential energy just before electron reaces te contact E ev Φ 0 Potential difference V
V stop E 0 Φ e Linear in frequency E 0 f V stop e f Φ e Same slope for all materials: measure, find 6.6 10 34 J sec Material-dependent intercept Φ e
Compare Compton scattering for x rays λ0pm and visible ligt λ500nm at a particular angle of scattering. Wic as te greater (a) Compton sift, (b) fractional wavelengt sift, (c) fractional energy loss, and (d) energy imparted to te electron? λ mc ( 1 cosφ) Compton sift: same for everyting λ λ E E E E E f f f c / λ c / λ c / λ λ λ + λ Xrays E c c c λ λ λ ( λ + λ) λ
X rays wit poton energy 56 kev are scattered from a carbon target, and te scattered rays are detected at 85 to te incident beam. (a) Wat is te Compton sift of te scattered rays? λ mc ( 1 cosφ).pm (b) Wat percentage of te initial x-ray poton energy is transferred to an electron in suc scattering? Know cange in wavelengt, need wavelengt f c / λ E 56keV λ c / E pm E E E E E f f f c / λ c / λ c / λ λ λ + λ 0.09
Wat is te de Broglie wavelengt of an electron wit a kinetic energy K0 ev? p m K p λ mk λ 9 10 31 34 6.6 10 kg 0eV J s 10 3 10 m 19 1.6 10 J / ev Wat is te size of diffraction grating for tis electron to be diffracted? usually d 0. 1mm θ λ 10 6 rad d unobservable want θ 10 1 rad d 10A Interatomic spacing
Wat is te de Broglie wavelengt of a baseball traveling wit v90mp? p λ p mv λ 34.6 10 s 0.15kg 40m / s 6 J 34 10 m No possible diffraction
ligt particles I E I # particles I # potons I? Amplitude of some wave Matter waves Ψ( r, t) Probability to find particle at position r at time t Ψ( r, t) Probability density At eac time I can find my particle somewere Ψ( r, t ) dr # particles
Single particle wit definite energy E Ψ ( r, t) ψ ( r) e iωt ω ω π f E Just as for potons One-dimensional motion in potential U(x) d ψ ( x) 8π m + x dx [ E U ( x) ] ψ ( ) 0 Scrödinger s equation Free particle U(x)0, Ep /m d ψ ( x) 4π p + ψ ( x) 0 dx ψ ( x) Ae ikx + Be k πp / p / ikx A wave!!! λ / p Ψ( r, t) Ae + Be i( kx ωt ) i( kx ωt) Traveling rigt+ traveling left
Particle wit momentum p moving to te rigt Ψ( r, t) i Ae ( kx ωt), ) Ψ( r t A If you measured te momentum precisely, te particle can be found anywere in space wit equal probability Fix momentum/wavelengt, ave no idea of position: a good wave Example of Heisenberg s uncertainty principle p p p x y z x y z px x uncertainty in momentum uncertainty in position Cannot know (or measure) bot momentum and position exactly at te same time
An electron is moving along an x axis and tat you measure its speed to be.05 10 6 m/s, wic can be known wit a precision of 0.50%. Wat is te minimum uncertainty wit wic you can simultaneously measure te position of te electron along te x axis? p x mv x 1.9 10 4 kg m/s p x 0.005p x 9.4 10 7 kg m/s x p x 11nm 1 atom ~0.1nm, so it is 110 atomic sizes A baseball is it wit te speed of 90mp, wic can be known wit a precision of 0.50%. Wat is te minimum uncertainty wit wic you can simultaneously measure te position of te baseball along te x axis? Mass of a baseball m150g. p x mvx 0.15kg 40m/s 6kg m/s p x 0.005p 0.03kg m/s x x p x 3 10 33 m
Tunneling Classically: impossible to get troug Scrödinger s equation d ψ ( x) dx 8π m + x [ E U ( x) ] ψ ( ) 0 Finite transmission probability T 8π m bl e b ( U E) b Launc many electrons: some get troug, measure current
Seeing atoms
We produce a diffraction pattern on a viewing screen by means of a long narrow slit illuminated by blue ligt. Does te pattern expand away from te brigt center (te maxima and minima sift away from te center) or contract toward it if we (a) switc to yellow ligt or (b) decrease te slit widt? sinθ m mλ a λ yellow > λ blue Expand in bot cases