FI 3103 Quantum Physics

Transcription

1 FI 3103 Quantum Physics Alexander A. Iskandar Physics of Magnetism and Photonics Research Group Institut Teknologi Bandung General Information Lecture schedule Tutorial Teaching Assistant : Mr. Suhandoko D. Isro BSC A During the tutorial there will be several Quizzes and average mark of the Quizzes will taken as one of the component of the Final Mark Walk Out time : 0 minutes Textbook S. Gasiorowicz, Quantum Physics 3 rd ed., John Wiley 003 Alexander A. Iskandar 1

2 General Information Evaluation : A Midterm Exam (week 7) and a Final Exam Expected Exam Answer : Answer should show good understanding of the physical phenomena considered in the problem, as evident by sound arguments and clear and correct steps in finding the solution. The use of correct formulas and notation (vector and scalar, integrals, complex) and the right units. Final correct numerical value (if asked). Slide download (weekly basis): Alexander A. Iskandar 3 The Emergence of Quantum Physics Black Body Radiation Photoelectric Effect Compton Effect Alexander A. Iskandar Emergence of Quantum Physics 4

3 (Modern) Physics in early 0th century 19 th century physicists thought they had it all together. They had complete understanding of classical (Newton) mechanics that govern particles to planetary movement. Newton promoted the corpuscular (particle) theory of light. Particles of light travel in straight lines or rays, which explained sharp shadows, reflection and refraction Alexander A. Iskandar Emergence of Quantum Physics 5 (Modern) Physics in early 0th century They found that it turns out electricity and magnetism are one of the same interaction, and Maxwell realized that light is a wave. E 0 B 0 B E t E B 0J 0 0 t 1 E 0 v t H Further proved by interference and diffraction promoted by Huygens and Fresnel. Alexander A. Iskandar Emergence of Quantum Physics 6 3

4 (Modern) Physics in early 0th century They introduced the concept of thermal equilibrium, established heat as energy, introduced the concept of internal energy, created temperature as a measure of internal energy. Realized limitations: some energy processes cannot take place. Alexander A. Iskandar Emergence of Quantum Physics 7 (Modern) Physics in early 0th century But they were surprised to find that several new experimental results were very weird that could not be explained with classical physics. Modern physics is the story of these surprises, surprises that have changed the world beyond all recognition. Understanding of these surprises lead to a new physics : the (old) quantum physics. The following lecture will give you a summary of these unexplained phenomena. Alexander A. Iskandar Emergence of Quantum Physics 8 4

5 Blackbody radiation When matter is heated, it not only absorbs light, but it also spontaneously emits it. A blackbody is a cavity with a material that only emits thermal radiation. Incoming radiation is absorbed in the cavity. Blackbodies are interesting because their optical properties are independent of the material and only depend on the temperature. Alexander A. Iskandar Emergence of Quantum Physics 9 Blackbody radiation Alexander A. Iskandar Emergence of Quantum Physics 10 5

6 Wien s Displacement Law The spectral intensity I(l, T) is the total power radiated per unit area per unit wavelength at a given temperature. I Wilhelm Wien (Phys. 1911) Wien s displacement law: The maximum of the spectrum shifts to smaller wavelengths as the temperature is increased. Alexander A. Iskandar Emergence of Quantum Physics 11 Stefan-Boltzmann Law The total power radiated increases with the temperature: I Jozef Stefan Ludwig Boltzman P( T ) I( l, T ) dl e T This is known as the Stefan-Boltzmann law, with the constant σ experimentally measured to be W / (m K 4 ). The emissivity e (e = 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 Alexander A. Iskandar Emergence of Quantum Physics 1 6

7 Rayleigh-Jeans Formula Lord Rayleigh used the classical theories of electromagnetism and thermodynamics to show that the blackbody spectral distribution should be: Lord Rayleigh (Phys. 1904) James Jeans It approaches the data at longer wavelengths, but it deviates badly at short wavelengths. This problem for small wavelengths became known as the ultraviolet catastrophe and was one of the outstanding exceptions that classical physics could not explain. I Alexander A. Iskandar Emergence of Quantum Physics 13 Planck s Radiation Law Planck assumed that the radiation in the cavity was emitted (and absorbed) by some sort of oscillators. He used Boltzman s statistical methods to arrive at the following formula that fit the blackbody radiation data. Planck made two modifications to the classical theory: Max Planck (Phys. 1918) The oscillators (of electromagnetic origin) can only have certain discrete energies, E n = nhn, where n is an integer, n is the frequency, and h is called Planck s constant: h = J s. The oscillators can absorb or emit energy in discrete multiples of the fundamental quantum of energy given by E h Alexander A. Iskandar Emergence of Quantum Physics 14 7

8 Photoelectric Effects Hertz showed that when UV light is shone on a metal plate in a vacuum, it emits charged particles. Classical predictions: Electric field E of light exerts force F = -ee on electrons. As intensity of light increases, force increases, so KE of ejected electrons should increase. Electrons should be emitted whatever the frequency n of the light, so long as E is sufficiently large PhET: photoelectric H. Hertz For very low intensities, expect a time lag between light exposure and emission, while electrons absorb enough energy to escape from material. Alexander A. Iskandar Emergence of Quantum Physics 15 Photoelectric Effects The actual results Maximum KE of ejected electrons is independent of intensity, but linearly dependent on n For n < n 0 (i.e. for frequencies below a cut-off frequency) no electrons are emitted There is no time lag. However, rate of ejection of electrons depends on light intensity Alexander A. Iskandar Emergence of Quantum Physics 16 8

9 Einstein s Theory Einstein take Planck s theory one step further. Einstein suggested that the electromagnetic radiation field is quantized into particles called photons. Each photon has the energy quantum: E hn or, E with h/ An electron absorbs a single photon to leave the material. Conservation of energy yields: A. Einstein (Phys. 1905) h KE f R. Millikan where f is the work function of the metal (potential energy to be overcome before an electron could escape). Verified in detail through subsequent experiments by Millikan. Alexander A. Iskandar Emergence of Quantum Physics 17 Einstein s Theory Electrons are bound in the target material by electric forces, therefore they need some minimum energy before they will get ejected at all (i.e., ejected with zero kinetic energy) The energy of the incoming photon goes into freeing the electron and then whatever energy remains goes into giving the electron some kinetic energy The maximum kinetic energy can be measured by the stopping potential. KE max ev stop h f Alexander A. Iskandar Emergence of Quantum Physics 18 9

10 Thomson Scattering Thomson scattering is the elastic scattering of electromagnetic radiation by a free charged particle, as described by classical electromagnetism. It is just the low-energy limit of Compton scattering: the particle kinetic energy and photon frequency are the same before and after the scattering. This limit is valid as long as the photon energy is much less than the mass energy of the particle: hn << mc. J.J. Thomson Alexander A. Iskandar Emergence of Quantum Physics 19 Thomson Scattering The electric field of the incident wave (photon) accelerates the charged particle, causing it, in turn, to emit radiation at the same frequency as the incident wave, and thus the wave is scattered. In this non-relativistic case, the main cause of the acceleration of the particle will be due to the electric field component of the incident wave, and the magnetic field can be neglected. q Alexander A. Iskandar Emergence of Quantum Physics 0 10

11 Thomson Scattering The particle will move in the direction of the oscillating electric field, resulting in electromagnetic dipole radiation. The moving particle radiates most strongly in a direction perpendicular to its motion and that radiation will be polarized along the direction of its motion. Therefore, depending on where an observer is located, the light scattered from a small volume element may appear to be more or less polarized. q Alexander A. Iskandar Emergence of Quantum Physics 1 Thomson Scattering The electric fields of the incoming and observed beam can be divided up into those components lying in the plane of observation (formed by the incoming and observed beams) and those components perpendicular to that plane. Those components lying in the plane are referred to as "radial" and those perpendicular to the plane are "tangential", since this is how they appear to the observer. q Alexander A. Iskandar Emergence of Quantum Physics 11

12 Thomson Scattering The diagram on the right shows the radial component of the incident electric field causing a component of motion of the charged particles at the scattering point which also lies in the plane of observation. It can be seen that the amplitude of the wave observed will be proportional to the cosine of q, the angle between the incident and observed beam. I tot 1 cos q The intensity, which is the square of the amplitude, will then be diminished by a factor of cos (q). It can be seen that the tangential components (perpendicular to the plane of the diagram) will not be affected in this way. Alexander A. Iskandar Emergence of Quantum Physics 3 q Compton Scattering Compton (193) measured intensity of scattered X- rays from solid target, as function of wavelength for different angles. A. Compton (Phys. 197) Alexander A. Iskandar Emergence of Quantum Physics 4 1

13 Compton Scattering Compton found that the peak in scattered radiation shifts to longer wavelength than source. Amount depends on q (but not on the target material). A. Compton (Phys. 197) Alexander A. Iskandar Emergence of Quantum Physics 5 Compton Scattering Treating the light as particle (photon) which has momentum, Compton explains the results by assuming billiard ball in-elastic collisions between particles of light (X-ray photons) and electrons in the material. A. Compton (Phys. 197) Alexander A. Iskandar Emergence of Quantum Physics 6 13

14 Compton Scattering The photon momentum is derived from relativistic energy-momentum relation: E m c Using the definition of speed p E m v 0 pc de dp pc E A. Compton (Phys. 197) Since the speed of light is vacuum is always c, then the momentum of a photon is given by E h h m0, photon 0 E pc p, c l c c l 1 m 0 c 4 pc p c 1 c Alexander A. Iskandar Emergence of Quantum Physics 7 Compton Scattering A. Compton (Phys. 197) Conservation of momentum h pi ˆ i p f Pe Pe pi p f p li Conservation of energy h m c i e h f 1 4 P c m c Alexander A. Iskandar Emergence of Quantum Physics 8 e e i p f 14

15 Compton Scattering A. Compton (Phys. 197) l l l f i h mec Compton won the 197 Nobel Prize in Physics. 1 cosq Alexander A. Iskandar Emergence of Quantum Physics 9 15