Quantum physics Anyone who is not shocked by the quantum theory has not understood it. Niels Bohr, Nobel Price in 1922 (1885-1962) I can safely say that nobody understand quantum physics Richard Feynman Nobel Lecture, 1966, (1918-1988) PHY232 Remco Zegers zegers@nscl.msu.edu Room W109 cyclotron building http://www.nscl.msu.edu/~zegers/phy232.html
so far we have treated light as being waves and used that formalism to treat optics and interference we have seen that under extreme conditions (very high velocities) the Newtonian description of mechanics breaks down and the relativistic treatment designed by Einstein must be used. Now, we will see that the description of light in terms of waves breaks down when looking at very small scales. In addition, we will see that objects that we usually refer to as particles (like electrons) exhibit wave-phenomena. PHY232 - Remco Zegers - quantum physics 2
photoelectric effect when light hits a metal, electrons are released. By providing a voltage difference between the metal and a collector, these electrons are collected and produce a current. if light is described in terms of waves one would expect that (classical description): independent of the frequency of the light, electrons should be emitted if one waits long enough for sufficient energy to be absorbed by the metal the maximum kinetic energy depends on the intensity (more energy absorbed) the kinetic energy of the electrons is independent on the frequency (wavelength of the light) and only depends on the intensity electrons take a little time to be released since sufficient energy needs to be absorbed PHY232 - Remco Zegers - quantum physics 3
however one observes that: if the frequency of the light is too low, no electrons are emitted the maximum kinetic energy of the electrons is independent of the intensity. the maximum kinetic energy increases linearly with frequency the electrons are emitted almost instantaneously, even at very low light intensities These observations contradict the classical description. It suggest that energy is delivered to the electrons in the metal in terms of well-localized packets of energy. The photons in the light beam are thus seen as particles that deliver packets of energy (so-called energy quanta) to the electron it strikes. PHY232 - Remco Zegers - quantum physics 4
photo-electric effect The energy carried by a photon: E=hf h: planck s constant (h=6.63x10-34 Js) f: frequency with c=fλ The energy is localized in the photon-particle The maximum kinetic energy of a released electron: KE max =hf-φ with: φ: the workfunction (binding of electron to the metal) So only if hf>φ will electrons be released from the metal f c =φ/h : f c is the cut-off frequency λ c =c/f c =(hc)/φ: the cut-off wavelength see table 27.1 for work functions for various metals PHY232 - Remco Zegers - quantum physics 5
example light with a wavelength of 400 nm is projected on a sodium metal surface (φ=2.46 ev). a) what is the energy carried by a single photon? b) what is the maximum kinetic energy of the released electrons? c) what is the cut-off wave length for sodium? d) what happens if light with a wavelength of 600 nm is used? PHY232 - Remco Zegers - quantum physics 6
lon-capa do problems 12,13 from LC 11 PHY232 - Remco Zegers - quantum physics 7
particle-wave dualism So, is light a wave or particle phenomenon? experiment can be described by light as waves can be described by light as particles reflection X X refraction X X interference diffraction polarization X X X photo-electric effect X answer: it depends! PHY232 - Remco Zegers - quantum physics 8
question light from a far-away star is used to perform a double slit experiment. Approximately once per 10 minutes will a single photon from the star arrive at the double slit setup on earth. Which of the following is true? a) since light is a wave-phenomenon, an interference pattern will be seen on a screen placed behind the double slits. b) since only one photon arrives every 10 minutes, interference is not possible since one can hardly think of the light coming in as waves PHY232 - Remco Zegers - quantum physics 9
question instead of a light source, an electron gun firing electrons at high speeds is used in a double-slit experiment. which of the following is true? a) since electrons are massive particles, an interference pattern is not produced b) electrons are similar to photons; they exhibit both wave and particle phenomena. In this case, electrons behave like waves and an interference pattern is produced. PHY232 - Remco Zegers - quantum physics 10
A interference pattern P 1 P 1 B P 2 P 2 If one of the slits in a double slit experiment is closed one sees only a diffraction pattern from a single slit (P 1 ). If the other slit is opened and the first one closed, one sees only the diffraction pattern from the other slit (P 2 ). If both are opened, one does not simply see the sum of P 1 and P 2 (like in A), but the double-slit interference pattern (like in B). The reason is the following: Remember that the intensity (I) is proportional to the E-field squared: I~E 2 =E 02 cos 2 θ. In A, it is assumed that the intensities add: I sum =I 1 +I 2. However, one should add the E-fields (which can be positive or negative) and than squared, like in B: I sum =(E 1 +E 2 ) 2 where E 1 and E 2 are treated as vectors. PHY232 - Remco Zegers - quantum physics 11
A and if you think that you ve seen it all B let s assume I determine through which hole the photon (or electron) goes by placing a detector before the slits. Would I still observe an interference pattern like in B? Answer: no! By measuring the location of the photon, we have turned the light-wave into a particle and the interference pattern gets lost. PHY232 - Remco Zegers - quantum physics 12
Schrödinger s cat A cat is placed in a closed box. Inside the box a radioactive source is placed in which on average once per hour a radioactive decay takes place. If the decay takes place, a bottle of poison breaks, killing the cat. In quantum-physical sense, the cat is 50% dead and 50% alive after half an hour. Since we can t see it, it is in a superposition of those two states and there is a certain probability of being in one of either states. Only when we open the box, do we determine what state the cat is in. The observation is crucial to determine the state of the cat. PHY232 - Remco Zegers - quantum physics 13
PHY232 - Remco Zegers - quantum physics 14
heisenberg s uncertainty principle If we want to determine the location and velocity (momentum) of an electron at a certain point in time, we can only do that with limited precision. Let s assume we can locate the electron using a powerful light microscope. Light scatters off the electron and is detected in the microscope. However, some of the momentum is transferred and observing the electron means we can only determine its velocity (momentum) with limited accuracy. note ħ=h/(2π) ΔxΔp h/(4π) with Δx: precision of position measurement with Δp: precision of momentum (mv) measurement this can also be expressed in terms of energy and time measurements ΔEΔt h/(4π) with ΔE: precision of energy measurement with Δp: precision of time measurement PHY232 - Remco Zegers - quantum physics 15
example The location of an electron is measured with an uncertainty of 1 nm. One also tries to measure the velocity of the electron. What is the (minimum) uncertainty in the velocity measurement? The mass of the electron is 9.11x10-31 kg. note that the uncertainty principle works for the three dimensions separately: ΔxΔp x h/(4π) ΔyΔp y h/(4π) ΔzΔp z h/(4π) PHY232 - Remco Zegers - quantum physics 16
photons as particles and quanta Some other examples of where the particle nature of light plays a role: Photo-electric effect Black-body radiation bremmstrahlung Compton effect PHY232 - Remco Zegers - quantum physics 17
lon-capa do problem 4 from LC 12 PHY232 - Remco Zegers - quantum physics 18
black-body radiation A black body is an object that absorbs all electromagnetic radiation that falls onto it. They emit radiation, depending on their temperature. If T<700 K, almost no visible light is produced (hence a black body). The energy emitted from a black body: P=σT 4 with σ=5.67x10-8 W/m 2 K 4 The peak in the intensity spectrum varies with wavelength using the Wien displacement law: λ max T=0.2898x10-2 mk (classical) Until 1900, the intensity distribution, predicted using classical equations, predicted a steep rise at small wavelengths. However, the opposite was determined experimentally PHY232 - Remco Zegers - quantum physics 19
Planck to the rescue Max Planck devised a theory for a simple black body that could describe the measured spectra. He assumed that the walls consisted of little radiators that only emitted light at certain discrete energies: E=nhf f the frequency of the light (Hz) h: planck s constant (6.63x10-34 Js) n: integer. His achievement was really the first success of quantum theory In essence, his theory showed that because the energy is quantized, it is hard to emit light of small wavelengths (high frequency) since a lot of energy is required PHY232 - Remco Zegers - quantum physics 20
example Hot lava can be considered as a black body emitting radiation at a variety of temperatures. If temperature of molten lave is about 1200 0 C, what is the peak wave length of the light emitted? PHY232 - Remco Zegers - quantum physics 21
lon-capa do problems 8 and 9 of LC 11 PHY232 - Remco Zegers - quantum physics 22
X-rays when energetic electrons are shot on a material, photons with small wavelengths (~0.1 nm) are produced. The spectrum consist of two components broad bremsstrahlung spectrum peaks at characteristic wavelengths depending on the material (see next chapter) the bremsstrahlung (braking radiation) is due to the deflection of the electron in the field of the charged nucleus. a light quantum is produced when the electron is deflected. It takes away energy from the electron PHY232 - Remco Zegers - quantum physics 23
bremmstrahlung assume electrons are accelerated in a potential of V Volts. their kinetic energy is E=eV with e=1.6x10-19 C and V the potential If the electron is completely stopped in the material, all its kinetic energy is converted into the photon with maximum frequency f max and hence minimum wavelength λ min if it merely deflected, the frequency f is smaller than f max and its wavelength λ larger than λ min. so ev=hf max =hc/λ min PHY232 - Remco Zegers - quantum physics 24
example an X-ray spectrum is analyzed and the minimum wavelength is found to be 0.35 angstrom (1 angstrom: 10-10 m). What was the potential over which the electrons were accelerated before the interacted with the material? PHY232 - Remco Zegers - quantum physics 25
Braggs law X-rays scattered off atoms in e.g. will interfere and the interference pattern can be used to identify/study materials. PHY232 - Remco Zegers - quantum physics 26
question X-rays are sometimes used to identify crystal structures of materials. this is done by looking at the diffraction pattern of X-rays scattered off the material (see ch 27.4). Why are X-rays used for this and not for example visible light? a) the wavelength of X-rays is close to the spacing between atoms in a crystal b) since the frequency (and thus energy) of X-rays is much larger than that of visible light, they are easier to detect c) X-rays are much easier to produce than visible light PHY232 - Remco Zegers - quantum physics 27
lon-capa do problem 10 of LC 11 PHY232 - Remco Zegers - quantum physics 28
compton effect When photons (X-rays) of a certain wavelength are directed towards a material, they can scatter off the electrons in the material If we assume the photon and the electron to be classical particles, we can describe this as a normal collision in which energy and momentum conservation must hold. after taking into account relativistic effects (see previous chapter) one finds that: PHY232 - Remco Zegers - quantum physics 29
compton scattering Δλ=λ-λ 0 =h/(m e c) x (1-cosθ) with: λ: wavelength of photon after collision λ 0 : wavelength of photon before collision h/(m e c): Compton wavelength (2.43x10-3 nm) m e : mass of electron θ: angle of outgoing X-ray relative to incoming direction λ λ 0 PHY232 - Remco Zegers - quantum physics 30
Δλ=λ-λ 0 =h/(m e c) x (1-cosθ) example A beam of X-rays with λ 0 =10-12 m is used to bombard a material. a) What is the maximum shift in wavelength that can be observed due to Compton scattering? b) What is the minimum shift in wavelength that can be observed due to Compton scattering? c) What are the minimum and maximum kinetic energies of the struck electrons, ignoring binding to the material they are in. PHY232 - Remco Zegers - quantum physics 31
lon-capa do problem 14 from lon-capa 11 PHY232 - Remco Zegers - quantum physics 32
applications PHY232 - Remco Zegers - quantum physics 33