Photoelectric Effect & Bohr Atom

Transcription

1 PH0008 Quantum Mechanics and Special Relativity Lecture 03 (Quantum Mechanics) v2 Photoelectric Effect & Bohr Atom Prof Department of Physics Brown University Main source at Brown Course Publisher background material may also be available at Gaitskell

2 Section: Quantum Mechanics Week 1 START OF WEEK THIS WEEK NEXT WEEKEND Homework (due for M 4/1) o [SpecRel] Done Reading (Prepare for 4/1) o SpecRel for Exam Revise Ch2-6 (look at Ch 1 also) o QuantMech Ch1,2 & 3 Lecture 01 (M 4/1) o Quantum Mechanics Introduction Photoelectric Effect Demo Lecture 02 (W 4/3) o Quantum Mechanics Photoelectric Effect Blackbody Radiation Reading (Prepare for 4/8 after recess) o SpecRel Revise o QuantMech Ch1,2 & 3 No Homework (M 4/8) o Revision for Exam (M4/8) Homework #9 (M 4/15) o (see web Assignments ) Lecture 03 (F 4/5) o Quantum Mechanics Atomic Line Spectra Bohr Atom

3 EXAM II PLEASE ARRIVE 8.20 AM ON MONDAY o ROOM 168 o No Calculators

4 Question Section

5 Classical Physics in Crisis

6 The Birth of Modern Physics Experiments that were at odds with Classical Model of Physics (around 1900) o Problems for both Newtonian physics, and purely wave theory of light Those we will consider o Photoelectric Effect o Blackbody Radiation o Atomic Line Spectra Further experiments that study QM effects o Davisson-Germer (1925) Electron ( ev) scattering from surface of single crystal metal o GP Thomson (1927) Electron (10-40 kev) transmission through micro-crystalline foils o Double Slits - Single Photons (1909 )

7 Review

8 Blackbody (thermal) Radiation

9 Blackbody Spectrum Observed vs Rayleigh-Jeans <- Ultraviolet Catastrophe! (shorter wavelengths) Radiancy R( l) [Wcm -2 nm -1 ] 5500 K Observed Blackbody Spectra at two different temperatures 4000 K Rayleigh-Jeans Theory (dashed) Derived from Classical EM & Thermodynamics R( l) ~ l 4 Note: Classical theory does agree with observation at long wavelengths But, rapid divergence as l->0 Wavelength l [nm]

10 Planck 1900 Resolving Crisis: The beginning o Suggest that if it is assumed that energy of normal mode is quantised such that E=hn (h is an arbitrary constant, Planck s arbitrary constant, experimentaly determined so that theory fits data) then higher frequency (shorter wavelength) modes will be suppressed/eliminated. o Planck suggests ad hoc that the radiation emitted from the walls must happen in discrete bundles (called quanta) such that E=hn. Mathematically this additional effect generates an expression for spectrum that fits data well. The Planck constant is determined empirically from then existing data The short wavelength modes are eliminated o In a classical theory, the wave amplitude is related to the energy, but there is no necessary link between the frequency and energy Classically one can have low freq. waves of high energy and vise versa without constraint Planck is unable to explain how such an effect could come about in classical physics Einstein 1905 o Based on Photoelectric effect, Einstein proposed quantisation of light (photons) Photons are both emitted and absorbed in quanta

11 Photoelectric Effect

12 Experimental Setup (1) Illumination of Photoelectric material in vacuum 2nd Electrode Photoelectric Material I V o Electromagnetic waves couple to electrons Ejecting some of them from material if they are given sufficient energy to overcome binding into material (known as work function ) Ejected electrons have a range of Kinetic Energies

13 Experimental Setup (2) +ve bias on sense electrode 2nd Electrode Photoelectric Material I + V o Bias accelerates electron toward sense plate

14 Experimental Setup (3) ve bias on sense electrode 2nd Electrode Photoelectric Material I V + o Voltage raised to the a level where Potential overcomes Kinetic Energy of ejected electron Current measured falls to zero

15 Experimental Setup (4) - Classical Interpretation Response to different incoming wave intensities o (Note that this turns out to be wrong ) 2nd Electrode Smaller KE Larger KE I V

16 Experimental Setup (5) - Classical Interpretation Response to different incoming wave intensities - apply ve bias 2nd Electrode Smaller KE Larger KE I V + o Voltage raised to the a level where Potential overcomes Kinetic Energy of ejected electron Current measured falls to zero, we can use the Voltage as an Energy Spectrometer

17 Experimental Setup (6) - Electron Potential Diagram Voltage as an Energy Spectrometer - apply ve bias 2nd Electrode Smaller KE Larger KE I Increasing KE elec I 1 Potential Energy of electron V + + -V 0 I 2 > I 1

18 Light Sources Filters - approximate band-pass o Red nm o Green nm o Blue nm Wavelength 700nm 600nm 500nm 400nm Visible Wavelength Spectrum from

19 Summary of Results For given wavelength, vary intensity For given intensity, vary wavelength Look at V 0 vs Frequency Increasing KE elec I 2 I 1 -V 0 + I 2 > I 1 Increasing KE elec + -V 0 -V n 0 n 1 Increasing KE elec + n 2 -V 0 blue red green -V 0 blue > red n 2 > n 1 -V frequency n=c / l -V 0 > -V 0

20 Experimental Setup (4b) - QM Interpretation Response to different incoming photon energies 2nd Electrode Smaller KE Larger KE I V o Voltage raised to the a level where Potential overcomes Kinetic Energy of ejected electron Current measured falls to zero

21 Experimental Setup (5b) - QM Interpretation Response to different incoming photon energies - apply ve bias 2nd Electrode E photon = hn = K electron + f n red < n blue E red < E blue Smaller KE Larger KE I V + o Voltage raised to the a level where Potential overcomes Kinetic Energy of ejected electron Current measured falls to zero

22 Photoelectric Effect (Conclusion 1) Puzzles for Classical Physics o V>V o retarding potential appears to stop all electrons independent of the intensity So maximum Kinetic Energy of ejected electrons does not depend on intensity? but classically we expect greater intensity would lead to higher kinetic energies? There does appear to be a dependence on wavelength Shorter wavelength light gives electrons which require greater potentials to stop o What is n 0 the minimum light frequency below which no electrons are ejected from a given material? We can accept idea that there is some kind of energy threshold for extraction of an electron from material but classically we would expect only intensity threshold? If longer wavelength light seems to have no effect, then just turn up intensity until it does?? o Why is ~no time delay for emission of electrons when intensity very low Expect delay in emission while field builds up for very low intensity case?

23 Summary of Results (2) Look at V 0 vs Frequency Increasing KE elec -V 0 + E photon = hn = K electron + f K electron = ev 0 V 0 = hn - f e = h ( e n -n 0) n 0 n blue red green frequency n=c / l f Energy to extract electron from material K electron Kinetic Energy of Electron V 0 retarding potential used to measure KE h apparent slope of voltage vs freq. graph e n frequency of light illuminating n 0 work function re- expressed as freq. on intercept V 0 K electron f

24 Light Sources (2) - Energy Equivalents & h Filters - approximate band-pass o Red ev o Green ev o Blue ev Wavelength 700nm 600nm 500nm 400nm E = hn = hc l = 1240 ev nm l Energy 1.8eV 2.1eV 2.5eV 3.1eV h = Js = evfs hc = Jm = evnm = evmm 1 ev is the potential energy change for an electron 0 Æ1 V 1 ev = qv q = C V =1 V 1 ev = VC = J Visible Wavelength Spectrum from

25 Electromagnetic / Photon Spectrum 700nm 600nm 500nm 400nm Energy 1.8eV 2.1eV 2.5eV 3.1eV

26 Photoelectric Effect (Demo 1) - Review Preliminary Demonstration o Zn plate on electrometer illuminated by Carbon Arc Lamp Charge Zn plate using physical transfer from electrostatic build up of electrons on PVC o Illumination -> observe effect on charge using electrometer (1) Direct Illumination (2) Through standard glass (blocks UV) (3) Through quartz (block any particles, but not optical or UV photons) Details o Zn work function f~4.3 ev o UV light ~290 nm (=4.3 ev) E = hn = hc l ev nm = 290 nm = 4.3 ev h = Js = evfs hc = Jm = evnm = evmm

27 Photoelectric Effect (Conclusion 2) Resolution - Einstein 1905 o Radiation is composed of bundles of energy Photons, each with energy = hn Total energy of beam of radiation is nhn where n is # of photons o Identify n 0 with the work function f of the metal f = hn 0 f is energy needed to liberate the loosest bound electron o Incident photon - energy hn = f + K max. o V 0 is independent of I Intensity only affects the # of photons, not the individual energies o Time Delay Photons (bundles of energy) arrive immediately, so electron can be ejected immediately

28 Atomic Transitions: Quantized

29 Line Spectra If we create a system where atoms are nearly independent o Gas discharge at low pressure o Dl / l ~ 10-5 But the relative position of these lines is very complex o Best hope was to look at lines seen from Hydrogen o Balmer (1885) creates a very accurate mathematical model for position Have to wait for theoretical work of Bohr (1913) to provide some insight Note o 1864 Maxwell showed light is electromagnetic radiation o 1887 Hertz demonstrates that radiation is emitted by accelerating charges o 1897 JJ Thomson discovers electron Proposes plumb-duff model of electrons embedded in large positive core

30 Emission & Absorption Spectra Graphics from Dr Mike Guidry Univ Tennessee

31 Emission & Absorption Spectra (2) Graphics from Dr Mike Guidry Univ Tennessee

32 Balmer - Empirical Relationship (1885)

33 Balmer Series Balmer Series o Swiss mathematician (for which he is not remembered!) used his analytical skills to see that the wavelengths of Hydrogen emission series are well fitted by Higher Energy Lower Energy n 2 l n = Å (m = 2, n = 3,4,5,6...) n m First 4 values in series , , ,

34 Balmer Series IR Deep IR UV Optical Higher Energy Lower Energy