Lecture 16 Quantum Physics Chapter 28

Transcription

1 Lecture 16 Quantum Physics Chapter 28

2 Particles vs. Waves Physics of particles p = mv K = ½ mv2 Particles collide and do not pass through each other Conservation of: Momentum Energy Electric Charge Physics of Waves Carries energy Intensity is proportional to amplitude of wave Total Energy depends on intensity and duration Waves pass through one another Interference 2

3 Particles and Waves Electrons exhibiting interference when sent through a double slit 3

4 Properties of waves and particles All objects, including light and electrons, can exhibit interference All objects, including light and electrons, carry energy in discrete amount These discrete parcels are called quanta Hence quantum physics Usually only detect wavelike nature of objects that are small melectron = 9.1 x kg ratom.1 nm Things that exhibit both particle and wave properties are said to be in the quantum regime We'll be more specific about what this means later 4

5 Photoelectric Effect Intro The quantum nature of light was first discovered through the Photoelectric Effect 1880's Electrons are free to move around in the metal With a high enough E-field, they jump off Voltage corresponds to an energy V = PEelec / q Minimum required energy to free an electron is called the Work Function Wc = e V 5

6 Work Function of Metals 6

7 Photoelectric Effect Another way to extract electrons from a metal is by shining light onto it Light striking a metal is absorbed by the electrons If an electron absorbs an amount of light energy greater than Wc, it is ejected off the metal This is called the photoelectric effect 7

8 Expectation vs. Reality Expectation: If light is a wave you should be able to carry more energy to the electron by increasing the amplitude of the wave If no electrons are escaping, making the light brighter should allow electrons to escape Reality: Electrons ability to escape depends only on the frequency of light striking the metal Ejected only when frequency is above fc, the critical frequency Energy of the ejected electrons continues to increase with the frequency of light 8

9 Einstein Explains the Photoelectric Effect Einstein proposed that light carries energy in discrete quanta, now called photons Each photon carries a parcel of energy Ephoton = hƒ A beam of light should be thought of as a collection of photons h is a constant of nature called Planck s constant h = x J s Each photon has an energy dependent on its frequency If the intensity of monochromatic light is increased, the number of photons is increased, but the energy carried by each photon does not change Historical Irony Einstein won Nobel Prize for his explanation of the photoelectric effect He didn't win for Relativity because too many people objected to his findings Einstein would later object to the findings of quantum theory 9

10 Photoelectric Effect Explained An incoming photon has energy Ephoton = hƒ If hƒ > Wc the electron is ejected otherwise nothing happens Critical frequency is fc = Wc / h Any excess energy will become the ejected electron's kinetic energy KEelectron = h ƒ - Wc 10

11 Momentum of Photon Maxwell predicted that EM waves carry momentum (Ch. 23) Momentum of a photon p=e/c p = hf / c = h / λ Photons are particles of light They have a defined Energy and Momentum Even though they don't have mass They can collide with other particles But light is still a wave Interference Wave-particle duality 11

12 Biology Aside Highly energetic photons can damage tissue and cause cancer UV radiation skin is our protection, but it can cause skin cancer X-rays It's why you have to wear a heavy smock Gamma rays Are bad in large doses, but most simply pass through us Radio waves Generally harmless Cell Phones Studies? Con: How these waves be harmful and visible light be fine when visible light is far more energetic? Pro: Cell phones are a much more intense source of photons. Damage depends on intensity and exposure time. 12

13 How many photons does a laser emit? Classic problem A red laser pointer has a power rating of 1 mw Red = 660 nm W (power) = J/s Laser produces.001 Joules per second How many red photons will add up to get.001 J? Tips on Units Sometimes the energy of a photon is given in electron-volts (ev) Energy of a visible photon is between 1.5 and 3 ev Lasers are labeled in SI units E = hf will give an answer in SI units because we gave you h in SI units 1 ev = x J 13

14 Blackbody Radiation Blackbody radiation Hot things start to glow Color is described by Wein's Law λ = 2.9 x 10-3 m K / T Obtained purely from observation Light from hot objects can be described in terms of standing waves Phys 220 wave on a string fn = nf1 Classical Physics f1 is the fundamental frequency Infinite allowed frequencies = infinite intensity Ultraviolet catastrophe Planck's idea (1901) Energy of the standing wave is quantized E = hfn Statistical mechanics solves the problem then Not quite photons but getting there... 14

15 De Broglie Wavelength Blackbody radiation and the photoelectric effect are instances of light behaving like a particle instead of a wave What about things that are thought of as particles behaving like waves? Louis de Broglie's idea Momentum of photon: p = h / λ Wavelength of massive particles: λ = h / p = h / mv 15

16 Electron Interference To test de Broglie s hypothesis, an experiment was designed to observe interference involving classical particles The experiment showed conclusively that electrons have wavelike properties The calculated wavelength was in good agreement with de Broglie s theory 16

17 Wavelengths of Macroscopic Particles From de Broglie s equation and using the classical expression for kinetic energy h λ= = p h 2m(KE ) As the mass of the particle (object) increases, its wavelength decreases In principle, you could observe interference with baseballs Has not yet been observed 17

18 Why don't we see baseballs interfering? Wavelength of a 1000 V electron KE = (1000 V)(1.609 x C) λ = nm Slits of crystal.1 nm wide Single slit diffraction θ λ / w =.1 radians This is measurable Wavelength of a 100 mph baseball p = mv = (.150 kg)(44 m/s) = 6.6 kg m/s λ = m 10 cm slits (so that a baseball can fit through) θ λ / w = radians This is not mesurable Unless your screen is a trillion light years away 18

19 Quantum Regime The quantum regime refers to objects that have an observable De Broglie wavelength Right now the smallest distances we can measure are about meters Theoretical limit to shortest distance possible.1 attometer Planck Length: meters If the De Broglie wavelength is too small to measure, then so will effects due to interference Large objects generally have very short De Broglie wavelengths We can ignore their wave-like nature 19

20 Other things can be quantized Electrons have another quantum property that involves their magnetic behavior An electron has a magnetic moment, a property associated with electron spin Classically, the electron s magnetic moment can be thought of as spinning ball of charge 20

21 Electron Spin The spinning ball of charge acts like a collection of current loops This produces a magnetic field It acts like a small bar magnet Therefore, it is attracted to or repelled from the poles of other magnets 21

22 Stern-Gerlach Experiment When two bar magnets come together, like poles repel and different poles attract But it depends on orientation S N S N attracts S N S N repels N N S No attraction or repulsion S The Stern-Gerlach experiment sent an electron beam by a magnet to detect the electron's magnetic moment. The electron beam split into two upon passing the magnet suggesting only two possible orientations. The spin of the electron is quantized. 22

23 Wavefunctions Like in relativity Newton's laws fail to explain behavior in the quantum regime The quantum version of Newton's Laws is called the Schrödinger equation Developed by Erwin Schrödinger, one of the inventors of quantum theory Newton's Laws give answers to position, velocity, acceleration, momentum, energy, etc. The Schrödinger equation gives a particle's wavefunction The wavefunction contains all that information 23

24 Wavefunction: Properties and meaning An electron is confined to a particular region of space A classical particle would travel back and forth inside the box The wave function for the electron is described by standing waves Like a wave on a string Two possible waves are shown Each represents a different energy state Fixed at both ends Just like light, higher energy = shorter wavelength Wavefunction squared gives probability of finding a particle at a particular point Light: Amplitude squared gave intensity = # of photons at a given point 24

25 Exact location of the particle in the box? For a particle-wave, quantum effects place fundamental limits on the precision of measuring position or velocity The standing waves are the electron, so there is an inherent uncertainty in its position There is some probability for finding the electron at virtually any spot in the box The uncertainty, Δx, is approximately the size of the box This uncertainty is due to the wave nature of the electron 25

26 Uncertainty from a single slit Electrons are incident on a narrow slit The electron wave is diffracted as it passes through the slit The interference pattern gives a measure of how the wave function of the electron is distributed throughout space after it passes through the slit The width of the slit affects the interference pattern The narrower the slit, the broader the distribution pattern Less uncertainty in Δx = More uncertainty in Δpx 26

27 Heisenberg Uncertainty Principle The Heisenberg Uncertainty Principle gives the lower limit on the product of Δx and Δpx h Δ x Δ p x 4π The relationship holds for any quantum situation and for any wave-particle If you measure a particle-wave s position with great accuracy, you must accept a large uncertainty its momentum If you know the momentum very accurately, you must accept a large position uncertainty You cannot make both uncertainties small at the same time 27

28 Uncertainty Principle for time There is also a relationship between the uncertainties in the energy ΔE of a particle and the time interval Δt over which this energy is measured or generated The Heisenberg energy-time uncertainty principle is h Δ E Δ t 4π The uncertainty in energy measured over a time period is negligibly small for a macroscopic object 28

29 Linewidth of a laser Laser frequencies can be known to very high precision (ie Hz +/- 103 Hz) Good for precision measurements Accurate to one part in 1 in 100 billion Linewidth refers to the +/- part Uncertainty in laser frequency Pulsed lasers have an inherent uncertainty due to their short duration (h f)( t) h/(4π) What's linewidth of a picosecond (10-12 s) pulse? Could measure linewidth with a diffraction grating Femtosecond (10-15 s) pulses Length of pulse is shorter than a wavelength 29

30 Uncertainty Summary Quantum theory and the uncertainty principle mean that there is always a trade-off between the uncertainties It is not possible, even in principle, to have perfect knowledge of both x and p This suggest that there is always some inherent uncertainty in our knowledge of the physical universe Quantum theory says that the world is inherently unpredictable For any macroscopic object object, the uncertainties in the real measurement will always be much larger than the inherent uncertainties due to the Heisenberg uncertainty relation Ex. best measurement of position you can make with a ruler is to within.5 mm 30

31 3 Law of Thermodynamics rd According to the Third Law of Thermodynamics, it is not possible to reach the absolute zero of temperature In a classical kinetic theory picture, the speed of all particles would be zero at absolute zero There is nothing in classical physics to prevent that In quantum theory, the Heisenberg uncertainty principle indicates that the uncertainty in the speed of a particle cannot be zero The uncertainty principle provides a justification of the third law of thermodynamics 31

32 Tunneling According to classical physics, an electron trapped in a box cannot escape However the wavefunction can extend beyond the barrier You might find the electron outside of it's enclosure A quantum effect called tunneling allows an electron to escape under certain circumstances 32

33 Scanning Tunneling Microscope A scanning tunneling microscope (STM) operates by using tunneling A very sharp tip is positioned near a conducting surface If the separation is large, the space between the tip and the surface acts as a barrier for electron flow 33

34 Scanning Tunneling Microscope, Cont. The barrier is similar to a wall since it prevents electrons from leaving the metal If the tip is brought very close to the surface, an electron may tunnel between them This produces a tunneling current By measuring this current as the tip is scanned over the surface, it is possible to construct an image of how atoms are arranged on the surface The tunneling current is highest when the tip is closest to an atom 34

35 STM image 35

36 The Nature of Quanta The principles of conservation of energy, momentum, and charge are believed to hold true under all circumstances Must allow for the existence of quanta The energy and momentum of a photon come in discrete quantized units Electric charge also comes in quantized units The true nature of electrons and photons are particle-waves 36

37 Puzzles about Quanta The relation between gravity and quantum theory is a major unsolved problem Why are there two kinds of charge? No one knows how Planck s constant enters the theory of gravitation or what a quantum theory of gravity looks like Why do the positive and negative charges come in the same quantized units? What new things happen in the regime where the micro- and macroworlds meet? How do quantum theory and the uncertainty principle apply to living things? 37