# A potential difference V is maintained between the metal target and the collector cup Electrons ejected from C travel to A and G detects the flow Apply.

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A potential difference V is maintained between the metal target and the collector cup Electrons ejected from C travel to A and G detects the flow Apply voltage V between A and C to slow the ejected electrons down When potential matches the initial KE of the electrons, the flow stops (most energetic electrons stopped) K max = e V stop i

Photoelectric Effect V stop does not depend on the intensity of the light source for a given frequency f => classical physics would predict that if we increase the amplitude of the alternating electric field, then a larger kick would be given to the electron? => if light is composed of photons, then the maximum energy that an electron can pick up is that of a single photon

High intensity Low intensity Adjust V in negative sense until current vanishes K max = e V stop Independent of intensity! All electrons reach collector Measure V stop as a function of frequency f

Photoelectric Effect In each case, there is a minimum frequency f 0 for the effect to occur cannot be explained classically V stop f f0f0 Different metals

Photoelectric Effect Classical theory: oscillating e/m fields in the light cause electrons in the metal to oscillate average KE ~ amplitude 2 ~(electric field) 2 ~Intensity Quantum theory: light composed of energy packets called photons E=hf =>an electron absorbs one photon and gains energy hf (this process is independent of the intensity) not expected classically! => increase intensity or wait longer for electron to absorb enough energy

Photoelectric Effect Electron needs a minimum amount of energy  to escape  depends on the type of metal => called the work function if an electron absorbs a photon, then (hf -  ) is the amount of energy left over for KE e PE  Why do electrons stay in metals? Electrical force lowers the potential energy

Photoelectric Effect Hence we need hf >  to just escape that is f >  /h =f 0 Einstein: K max = (hf -  ) if no other = e V stop losses of energy are involved V stop =(h/e) f - (  /e) Slope =h/e is independent of the metal!

units: volts is a unit of electrical potential eV = (1.6x10 -19 ) volts is a unit of energy called an electron volt (eV) eV stop =h f -  = h( f - f 0 ) = K max

Problem A satellite in Earth orbit maintains a panel of solar cells of area 2.60 m 2 oriented perpendicular to the direction of the Sun’s rays. Solar energy arrives at the rate of 1.39 kW/m 2 (energy/area/time) (a) at what rate does Solar energy strike the panel? rate=energy/time = 1.39(2.60) =3.61 kW (b) at what rate are Solar photons absorbed ? ( =550nm) each photon carries E=hc/ =(6.63x10 -34 )(3x10 8 )/(550x10 -9 )=3.61x10 -19 J photons/time = (3.61x10 3 )/(3.61x10 -19 ) = 10 22 /sec

Problem (c) how long would it take for a mole of photons to be absorbed? N A = 6.02 x 10 23 time = N A /(number photons/time) = (6.02 x 10 23 )/10 22 = 60.2 sec

Problem Light strikes a sodium surface and causes photoelectric emission. If V stop = 5.0 volts and the work function  is 2.2 eV, what is the wavelength of the light? E photon = hf = hc/ Kmax = E photon -  = hc/ -  = e V stop = (hc)/(e V stop +  ) h = 6.63x10 -34 J.s = 6.63x10 -34 /1.6x10 -19 eV.s = 4.14 x10 -15 eV.s = (4.14 x10 -15 eV.s)(3x10 8 m/s)/[5.0 eV+2.2 eV] =170 nm

Momentum 1916 Einstein extended the photon idea when light interacts with matter, not only energy but also linear momentum is transferred via photons momentum is also transferred in discrete amounts p=hf/c = h/ photon momentum E=hf = hc/ p=hf/c= h/ => E = pc recall that E 2 =p 2 c 2 + m 2 c 4 => m=0 massless short wavelength photons have more energy and momentum!

Compton Effect 1923 Compton performed an experiment which supported this idea directed a beam of x-rays of wavelength onto a carbon target x-rays are scattered in different directions `  = 71.1 pm (10 -12 m) ` has 2 peaks

Compton Scattering Wavelength ` of scattered x-rays has two peaks these occur at and +   >0 is the Compton shift classical physics predicts  =0 Quantum picture: a single photon interacts with electrons in the target light behaves like a ‘particle” of energy E=hf=hc/ and momentum p=h/ => a collision

Compton Scattering Conservation of energy E = E` + K => E` f ` ` > X-ray momentum p=h/ p`= h/ ` electron momentum p e =  m e v E=hf=hc/ E`=hf `=hc/ ` K=m e c 2 (  -1)

Compton Scattering Conservation of energy E = E` + K => E` f ` ` > X-ray momentum p=h/ p`= h/ ` electron momentum p e =  m e v E=hf=hc/ E`=hf `=hc/ ` K=m e c 2 (  -1)

X-ray scattering Energy and momentum are conserved Momentum is a vector! F=dp/dt=0 => p = constant

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