PHY313 - CEI544 The Mystery of Matter From Quarks to the Cosmos Fall 2005

Transcription

1 PHY313 - CEI544 The Mystery of Matter From Quarks to the Cosmos Fall 2005 Peter Paul Office Physics D PHY313 Peter Paul 09/8/05 PHY313-CEI544 Fall-05 1

2 The Energy Scales of Matter ses/glossary/key_energies.html Energy units in the standard system is the Joule, 1 W = 1 J/s In advanced physics the energy unit is the ev, the energy it takes to accelerate one electric charge with a potential of 1 Volt. This unit is very small 1 ev = Joules 1000 ev = 1 kev 1 Million ev = 1 MeV 1 Billion ev = 1 GeV A 27-in TV accelerates electrons to 30 kev, The Relativistic Heavy Ion Collider accelerates Au ions to 100 GeV x 197 ~ 20 TeV about 1 Billion times your TV Peter Paul 09/8/05 PHY313-CEI544 Fall-05 2

3 What have we learned so far? Physics changed around the years 1900 to 1905 by the introduction of energy quantization by Planck and by Einstein s realization that the speed of light must be the same in all inertial reference frames. Thus h = 4.14 x ev s and c = 3 x 10 8 m/s became the two most important constants in nature. When a mass moves at v ~ c the laws must change from Newton s mechanics to Relativity. When an action involves an energy and scale close to hc = 1240 ev nm quantum effects become important. The concepts that explain matter and mass apply to a huge scale of lengths and energy, of which the small dimensions from nanometers (nm) to femtometer (fm) have become important to our daily life. Four known fundamental forces describe all interactions in nature. They differ hugely in their strength and range. They bind quarks into nuclei, nuclei into atoms, atoms into crystals and materials, and hold together the masses in the cosmos. At very high energies 3 of these forces approach the same strength. Why? Peter Paul 09/8/05 PHY313-CEI544 Fall-05 3

4 Planck s Constant h The two most important constants in Nature are: The speed of light c C = x 10 8 m/s Planck s constant h h = x J s or x ev s h is a very small amount of action h c = 1240 ev nm Relativity becomes important when velocity ~ c Quantum effects become important when energy x size ~ h c Example from chip design: Energy scale ~ 6 ev Size ~ 1240/6 nm ~ 200 nm This is a very practical dimension and poses limits for the chip industry. Peter Paul 09/8/05 PHY313-CEI544 Fall-05 4

5 Energy scale of microscopic matter Atoms ev to kev Materials 0.1 ev to 1 ev Nuclei MeV Elementary particles 100 MeV to GeV Largest existing accelerator (LHC) 16 TeV = 1.6 x 10 3 GeV Unification scale GeV Planck Energy 1.2 x GeV Thermal scales: Room temperature 1/40 ev Temperature of the sun surface 6000 degrees ~ 0.5 ev Temperature required to melt nuclei: 170 MeV = 2000 x Billions of the temperature at the surface of the sun Peter Paul 09/8/05 PHY313-CEI544 Fall-05 5

6 1905: The Year of Albert Einstein In 1905 Einstein produced 3 break-through papers: 1. Photoelectric effect: Light is an energy quantum that can be treated like a particle. E = h ν 2. Brownian motion: heat is kinetic energy of small particles moving in a medium: 3. Special Relativity: The speed of light must be the same in all inertial reference frame: E = mc 2 4. His Gedanken Experiments established a whole new way to gain physical insight Peter Paul 09/8/05 PHY313-CEI544 Fall-05 6

7 The Photo Effect Einstein introduced E = h ν to explain the Photo-effect. E is a quantum of light energy photon with frequency ν In this process a photon knocks out electrons from material surfaces and gives them kinetic energy. The capability of knocking them out depends only on the frequency, i.e. the energy of the photon, not on the number of photons that hit the surface. The energy of the light overcomes the binding energy (WF) of the electron in the material: p/kap28/photoeffect/ This experiment proves that light can act as a particle. The binding energy WF depends on the material and tells us about the binding energy of electrons inside crystals and surfaces. K = hν WF Peter Paul 09/8/05 PHY313-CEI544 Fall-05 7

8 Review: Properties of Waves A wave has a frequency ν= number of oscillations per s (in Hz), a wave length λ = distance from one peak to the next (in m or nm). A velocity v = λ ν. An amplitude A. For sound wave v s = 334 m/s in air When a supersonic planes velocity exceeds v s it outruns its own sonic boom! A man with a flashlight in a fast car can never do that! Velocity of light c must be the same in all uniformly moving frames Two or more waves of the same frequency or different frequencies can be added. They can be diffracted and interfere with each other: Young s Double slit experiment nglishversion.htm /2000/applets/twoslitsa.html Peter Paul 09/8/05 PHY313-CEI544 Fall-05 8

9 Special Relativity: The basics If light is an EM wave the laws of optics require that speed of light c in free space must be the same in all inertial reference frames. There can be no ether medium that carries the light. A light wave travels through empty space! Otherwise a fast-moving traveler could outrun her own image! hbase/relativ/star.html - c1 This had been confirmed earlier experimentally in 1879 by Michelson. nia.edu/more_stuff/flashlets/mmexpt 6.htm The deep basis for Special Relativity is that. The laws of physics should be the same in all inertial reference frames. EM wave has a frequency ν, a wavelength λ and a speed c. These parameters are related: λν = c If c = constant then an increasing ν requires a decreasing λ - c1 Peter Paul 09/8/05 PHY313-CEI544 Fall-05 9

10 The Basis for Einstein s Special Theory of Relativity Einstein's theory of special relativity results from two statements -- the two basic postulates of special relativity: The speed of light is the same for all observers, no matter what their relative speeds. The laws of physics are the same in any inertial (that is, nonaccelerated) frame of reference. This means that the laws of physics observed by a hypothetical observer traveling with a relativistic particle must be the same as those observed by an observer who is stationary in the laboratory. Given these two statements, Einstein showed how definitions of momentum and energy must be refined and how quantities such as length and time must change from one observer to another in order to get consistent results for physical quantities such as particle halflife. To decide whether his postulates are a correct theory of nature, physicists test whether the predictions of Einstein's theory match observations. Indeed many such tests have been made -- and the answers Einstein gave are right every time! These assumptions lead to a number of unexpected results Peter Paul 09/8/05 PHY313-CEI544 Fall-05 10

11 Moving clocks and time dilation If c is constant, then we must expect strange new physics when somebody moves at a velocity close to c. A moving clock observed by a stationary observer, ticks more slowly when velocity is close to c: t = t' 1 v 2 c 2 A fly lives 1 day inside a car. If the car moves at a velocity of v = 0.8 x c i.e. at 80% of the speed of light, the fly s lifetime as seen by a road observer will be t = t /0.6 = 1.67 days That means the fly seems to live longer as measured by the stationary observer. T is the clock time of the observer sitting in the moving frame T is the clock time of the observer at rest. u/more_stuff/flashlets/lightclock.swf The famous twin paradox: The twin that traveled in a spaceship at close to the speed of light, ages less than the one who stays behind. Peter Paul 09/8/05 PHY313-CEI544 Fall-05 11

12 The Amazing Atmospheric Mu Mesons Mu (µ) mesons are created in the upper Muons can be produced in particle atmosphere at h = 10 km at a rate of ~1 per reactions and accelerated rapidly to, cm 2 and sec. say, 30 GeV. They live on the average in their rest frame Their time dilation factor then will be t = 2.3 µs. They move with a speed of 0.98 c Their travel time over 10 km is 34 µs and 1 E 30,000MeV only 0.3 out 1 Million survive. = = = However with time dilation their life time v mc 100MeV 1 2 is 5 x 2.3 = 11.5 µs and 49,000 out of a c million survive. T = µ s = 690µ s Thus the muons live 690 µs as they fly through the stationary atmosphere Haefele and Keating Experiment in 1972 traveling around the globe. Peter Paul 09/8/05 PHY313-CEI544 Fall-05 12

13 Moving Objects and Length Contraction An object of length L that moves with a speed v ~ c will be seen by a stationary observer with its dimensions in the direction of motion shortened A car that is 5 m long at rest and travels at v = 0.8 c will be only L = 5m = 5m 0.6 = 0.3m L = L' 1 v2 c 2 A Soccer ball will be shaped like a football with the short axis in the flight direction. more_stuff/flashlets/lightclock.swf Peter Paul 09/8/05 PHY313-CEI544 Fall-05 13

14 How Long is the SLAC Accelerator? The SLAC electron linear accelerator at Stanford University is 2 miles long on the ground. How long does it appear to the electrons in the beam? L = 2 miles = 3,200 m The final beam energy is 30 GeV. Thus at the half point E = 15 GeV 1 v 2 c 2 = 0.5MeV 15,000MeV = Thus if I am riding on the electron beam through the accelerator it is only L = 3,200/3000 ~ 1m long! Thus it is quite easy to align the machine! Peter Paul 09/8/05 PHY313-CEI544 Fall-05 14

15 Energy and Momentum in Special Relativity In Newton s mechanics every particle has a kinetic Energy K and a momentum p: K = m 2 v 2 = p2 2m p = m v Because of the condition that c is the same in all frames, these rules need to be changed in Special Relativity u/lectures/mass_increase.html In Einstein s mechanics every particle has kinetic energy K, a momentum p, and a mass energy given by mc 2. Kinetic energy and mass energy add up to a total energy E: E = p c + m c E E 2 = mc Stationary particle = mc 1 2 v c 2 2 Moving particle That means that the moving particle gains mass as it speeds up. It actually becomes heavier Peter Paul 09/8/05 PHY313-CEI544 Fall-05 15

16 Some mass energies at rest and in motion Rest energy of electron 511 kev Rest energy of the muon 106 MeV Rest energy of pion 140 MeV Rest energy of proton MeV Rest energy of neutron MeV Rest energy of Au nucleus GeV Rest energy of U nucleus GeV Rest energy of Z boson 80 GeV A 30-GeV electron moves with v/c = Its mass is ~ 30 GeV A 200-GeV proton moves with v/c = Its mass is ~ 200 GeV.. Peter Paul 09/8/05 PHY313-CEI544 Fall-05 16

17 What about the mass of the Photon? Since a photon always moves with the speed of light, it must be a very special object. Its rest mass must be zero because it can never stand still! Einstein writes down for the energy of a particle: E 2 = p 2 c 2 + m 2 c 4 For p = 0 (i.e. particle at rest) this gives the famous equation E = mc 2 Thus for a photon with m = 0 E = pc With De Broglie p = h/λ (see slide 20) this gives: E = hν as Einstein had already postulated. Thus it all hangs together. Mass is Energy! Peter Paul 09/8/05 PHY313-CEI544 Fall-05 17

18 Doppler Effect and Red shift If a photon is emitted from a moving source in my direction, do I see any effect from the moving source, even though c is always the same? Yes, if the source is moving toward me, the source is pushing the photon in my direction. That adds energy to the photon. Since the energy of the photon is E = hν, the frequency ν increases. If the source, like a star, is moving away from me the photon loses energy and ν decreases. This is the famous Red Shift observed from receding stars and galaxies all across the Universe. esk/archive/releases/2004/07 Peter Paul 09/8/05 PHY313-CEI544 Fall-05 18

19 Decay of neutral mesons into 2 Photons γ 1 π0 γ 2 A π0 meson is unstable because it can decay into 2 photons. It so decays with a lifetime of ~ s after creation. What are the energies of the 2 photons? The π0 mass at rest is E = 140 MeV. Thus energy of each of two photons is half of that: Eg = 70 MeV The velocity of each photon is c. Its frequency is n = 70 MeV/h = 17 x 1021 Hz or 17 x 1012 GHz In 1935 Hideki Yukawa predicted the existence of a new particle, the pion. It comes in 3 flavors: π +,π -, π 0 12 years later, in 1947, C. F. Powell detected a particle in cosmic rays which fit Yukawa s hypothesis Peter Paul 09/8/05 PHY313-CEI544 Fall-05 19

20 The mechanics of quantal systems Atoms emit light in discrete steps. This means electrons inside the atom must be in discrete orbitals, which cannot be explained by classical physics. The size of the orbits is given by the Bohr radius R B = 5.3 x m, The emitted photons have energies of ~ 1 ev Thus R B x E ~ 5x 10-2 nm ev< h c and quantum physics must be applied! -c1 De Broglie Peter Paul 09/8/05 PHY313-CEI544 Fall-05 20

21 The Electron as a Wave Einstein says: p = E/c = h/ λ for a photon De Broglie turns it around λ = h/p for a particle. This trick ascribes wave properties to a particles. Proof: Davidson/Germer show experimentally that electron diffraction from metals is the same as that obtained from x-rays. However: Because of their mass electrons have a much shorter wave length than X-rays λ = hc 2mc 2 E = 1240eVnm 2mc 2 E For a 100 kev electron beam the wave length is λ = 392 x 10-5 nm ~ 4 pm This has led to high resolution electron microscopy. X-ray diffraction Electron diffraction Peter Paul 09/8/05 PHY313-CEI544 Fall-05 21

22 Modern Electron Microscopy Peter Paul 09/8/05 PHY313-CEI544 Fall-05 22

23 Electrons in Atoms Electrons are bound in atoms by the electromagnetic force exerted by the nucleus. The question right now is: how will they move around? If they remain bound in the atom with a certain energy of motion, does the fact that they must also be considered like waves, have any effect? It turns out that this fact alone leads to the conclusion that electrons can move around the nucleus only in certain discrete orbitals. Already in 1913 Niels Bohr came to that conclusion. At that time the wave character of electrons had neither been systematically postulated nor experimentally demonstrated. It meant that the orbitals of the electrons in atoms are quantized. Niels Bohr received the Nobel prize in 1922 Peter Paul 09/8/05 PHY313-CEI544 Fall-05 23

24 Electrons as Strings Assume electrons are confined in the atom over a distance L Let s look at it as a linear problem, a particle = a wave in a box. This is like a string of length L that is fixed at both ends. Plucking the string produces standing waves in the box, with discrete wavelengths: 1. λ = 2L 2. λ = L = 2L/2 3. λ = 2L/3 In general λ = 2L/n with n = 1,2,3 /lecture99_35.html We call n the principal quantum number of the system. Different values of n produce different energies inside the box: E = p2 2m = h 2 c 2 n 2 2mc 2 2L ( ) 2 As the electron jump form a higher n to a lower n it looses energy which is given off as discrete light quanta. Peter Paul 09/8/05 PHY313-CEI544 Fall-05 24

25 First Homework Set-rev, due Sept. 15, Describe briefly the 3 important discoveries that Einstein published in Who demonstrated that electromagnetic waves exist. What lead to the discovery that light was an electromagnetic wave? 3. Where was Max Planck s office when he discovered his quantum theory? ((hint: go to the web!) 4. Give the approximate dimensions of the Earth, an ant, an atom and a nucleus, with their appropriate dimensional prefixes. 5. A light-year is a distance. How long is it? (hint: a year = 31,536,000 s) 6. Name the four forces that we encounter in Nature and describe briefly what action they perform. Peter Paul 09/8/05 PHY313-CEI544 Fall-05 25

26 Second Homework Set, due Sept. 15, What is the evidence that photons can be treated like particles? 2. Why does the double slit exp t show that electrons can be treated like waves? 3. If you see a sleek sports car driving by on the road at a speed of 0.99c, would it look stunted, elongated or unchanged to you? Explain! 4. Where was De Broglie when he thought up his famous relationship between wavelength and momentum? 5. Explain why electron microscopy can observe objects that are much smaller than what can be seen with a light microscope. 6. Why do standing waves on a string lead to a quantization? Peter Paul 09/8/05 PHY313-CEI544 Fall-05 26