CHAPTER 3 The Experimental Basis of Quantum

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1 CHAPTER 3 The Experimental Basis of Quantum 3.1 Discovery of the X Ray and the Electron 3.2 Determination of Electron Charge 3.3 Line Spectra 3.4 Quantization 3.5 Blackbody Radiation 3.6 Photoelectric Effect 3.7 X-Ray Production 3.8 Compton Effect 3.9 Pair Production and Annihilation As far as I can see, our ideas are not in contradiction to the properties of the photoelectric effect observed by Mr. Lenard. - Max Planck, 1905 Development of quantum theory which began in 1900 with Max Planck and his explanation of Blackbody Radiation Quantum hypothesis was not only necessary to explain a number of experimental results, but a correct description of nature.

2 3.1: Discovery of the X Ray and the Electron X rays were discovered by Wilhelm Röntgen in Observed x rays emitted by cathode rays bombarding glass Electrons were discovered by J. J. Thomson in Observed that cathode rays were charged particles In the 1890s scientists and engineers were familiar with cathode rays. These rays were generated from one of the metal plates in an evacuated tube across which a large electric potential had been established. It was known that cathode rays could penetrate matter and were deflected by magnetic and electric fields.

3

4 Thomson s Cathode-Ray Experiment Thomson used an evacuated cathode-ray tube to show that the cathode rays were negatively charged particles (electrons) by deflecting them in electric and magnetic fields. Thomson s method of measuring the ratio of the electron s charge to mass was to send electrons through a region containing a magnetic field perpendicular to an electric field. e C/ kg m

5 Calculation of e/m by Thomson e m / C kg

6 3.2: Determination of Electron Charge Robert A. Millikan in 1911 Oil drop experiment

7 Calculation of the oil drop charge (Prob. 6-7)

8 3.3: Line Spectra grating grating a n=1 d sin n

9 3.3: Line Spectra

10 Spectra Series In 1885, Johann Balmer found an empirical formula for wavelength of the visible hydrogen line spectra in nm: Balmer series: (nm) (where k = 3,4,5 and k > 2) Rydberg Equation As more scientists discovered emission lines at infrared and ultraviolet wavelengths, the Balmer series equation was extended to the Rydberg equation:

11

12 3.4: Quantization Current theories predict that charges are quantized in units (quarks) of ±e/3 and ±2e/3, but quarks are not directly observed experimentally. The charges of particles that have been directly observed are quantized in units of ±e. The measured atomic weights are not continuous they have only discrete values, which are close to integral multiples of a unit mass.

13 3.5: Blackbody Radiation

14 3.5: Blackbody Radiation Blackbody radiation is theoretically interesting because the radiation properties of the blackbody are independent of the particular material.

15 Wien s Displacement Law The intensity (λ, T) is the total power radiated per unit area per unit wavelength at a given temperature. Wien s displacement law: The maximum of the distribution shifts to smaller wavelengths as the temperature is increased. (where max = wavelength of the peak)

16 Stefan-Boltzmann Law The total power radiated increases with the temperature: RT ( ) T T 4 4 This is known as the Stefan-Boltzmann law, with the constant σ experimentally measured to be W / (m 2 K 4 ). The emissivity є (є = 1 for an idealized blackbody) is simply the ratio of the emissive power of an object to that of an ideal blackbody and is always less than 1.

17 a) From Wien s displacement law: b) From Stefan-Boltzmann law: c)

18 Rayleigh-Jeans Formula (, T ) 2 ckt 1 4 4

19 Planck s Radiation Law (, T ) 2 2 ch 1 e 5 hc/ kt 1 En nhf E hf Quantum hypothesis makes it harder for oscillators at higher frequency to emit energy i.e. eliminated the ultraviolet catastrophe. Still believed that the EM waves behaved classically, but that the energy transfer process is quantized.

20 (, T ) 2 2 ch 1 e 5 hc/ kt 1 R( T) T T 4 4

21 3.6: Photoelectric Effect (photocathode) (cathode) (anode)

22 Work function The incident light gives electrons extra kinetic energy. The minimum extra kinetic energy that allows electrons to escape the material Work function. Work function is the minimum binding energy of the electron to the material

23 Experimental Results 1) The kinetic energies of the photoelectrons are independent of the light intensity. -V 0 is sufficient to stop all photoelectrons, no matter what the light intensity. 2) The maximum kinetic energy of the photoelectrons, for a given emitting material, depends only on the frequency of the light. A different retarding potential -V 0 is required for light of different frequency. 3) The smaller the work function φ of the emitter material, the smaller is the threshold frequency of the light that can eject photoelectrons. 4) When the photoelectrons are produced, however, their number is proportional to the intensity of light. 5) The photoelectrons are emitted almost instantly following illumination of the photocathode, independent of the intensity of the light. 1) 2)

24 Experimental Results 1) The kinetic energies of the photoelectrons are independent of the light intensity. 2) The maximum kinetic energy of the photoelectrons, for a given emitting material, depends only on the frequency of the light. 3) The smaller the work function of the emitter material, the lower is the threshold frequency of the light that can eject photoelectrons. No photoelectrons are produced below threshold frequency no matter what intensity. 4) When the photoelectrons are produced, however, their number is proportional to the intensity of light. 5) The photoelectrons are emitted almost instantly (< 3x10-9 s) following illumination of the photocathode, independent of the intensity of the light. 3) 4)

25 Classical Interpretation

26

27 Einstein s Theory

28 Einstein s Theory

29 Quantum Interpretation

30 3.7: X-Ray Production Can inverse of photoelectric effect also occur? Or, can electron give up it s energy to a photon? Answer: Yes, however photons can only be created or absorbed as complete units. A photon cannot give up part of it s energy, it must give up all of it. Consider an energetic electron passing through matter. The electron will lose kinetic energy and radiate photons This process is called bremsstrahlung, (German word for braking radiation. )

31 X-Ray Production Current passing through a filament produces copious numbers of electrons by thermionic emission. These electrons are focused by the cathode structure into a beam and are accelerated by potential differences of thousands of volts until they impinge on a metal anode surface The electrons produce X-ray photons by bremsstrahlung as they stop in the anode material. Conservation of energy means the maximum photon energy emitted cannot exceed the electron kinetic energy. The work function can be ignored since so small compared to the electron s K.

32 Inverse Photoelectric Effect

33 3.8: Compton Effect (Compton scattering)

34 Compton Effect

35 Compton Effect pm.

36 Compton Effect = 90 o

37 3.9: Pair Production and Annihilation If a photon can create an electron, it must also create a positive charge to balance charge conservation. In 1932, C. D. Anderson observed a positively charged electron (e + ) in cosmic radiation. This particle, called a positron, had been predicted to exist several years earlier by P. A. M. Dirac.

38 Pair Production

39 (Ex. 3-17) Pair Production in Empty Space? Show that a photon cannot produce an electron-positron pair in free space. Energy: hf E E E mc pc mc hf2 mc pc mc pc mc pc pc hf Momentum in x-axis: p cos pcos c cos cos hf pc pc pc pc Inconsistent and cannot simultaneously be valid!

40 Pair Production in Empty Space? Conversion of photon energy to matters in empty space is impossible.

41 Pair Production in Matter

42

43 Pair Annihilation

44 Pair Annihilation

45 PET (positron emission tomography) producing a pair of (gamma) photons moving in approximately opposite directions

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