Historical Development of Particle Properties of Waves: From Newton to Quantum Mechanics, Study notes of Introduction to Philosophy

Download Historical Development of Particle Properties of Waves: From Newton to Quantum Mechanics and more Study notes Introduction to Philosophy in PDF only on Docsity! Lecture 4. Particle properties of waves Outline: • Light: waves vs. particles • Photons • Photoelectric effect (demonstration of the energy of photons) Classical physics Relativistic mechanics, El.-Mag. (1905) Quantum mechanics (1920’s-) Relativistic quantum mechanics (1927-) v/c h/s S – the action=momentum×distance, units g×cm2/s Historical development Newton (Opticks, 1704): light as a stream of particles (corpuscles). Descartes (1637), Huygens, Young, Fresnel (1821), Maxwell: by mid-19th century, the wave nature of light was firmly established (interference and diffraction, transverse nature of e.-m. waves). Physics of the 19th century: mostly investigation of light waves; physics of the 20th century – interaction of light with matter. One of the challenges – understanding the “blackbody spectrum” of thermal radiation (to be considered later in the course). Planck (1900) suggested a solution based a revolutionary new idea: emission and absorption of electromagnetic radiation by matter has quantum nature: the energy of a quantum of e.-m. radiation emitted or absorbed by a harmonic oscillator with the frequency f is given by the famous Planck’s formula E h f= where h is the Planck’s constant 346.626 10h J s−≈ × ⋅ E ω=h where 341.05 10 J s−≈ × ⋅h2 fω π=Also, in terms of the angular frequency 2 h π =h - at odds with the “classical” tradition, where energy was always associated with amplitude, not frequency Photons According to the quantum theory of radiation, photons are massless bosons of spin 1 (in units ħ). They move with the speed of light : ph ph ph E h f E cp = = “Light” – a shorthand notation for any e.-m. radiation (ν from 0 to ∞). ( ) ( ) ( )22 2 2 0ph ph phE cp m c− = = Quantum character of this equation is illustrated by the fact that the energy is associated with the frequency of oscillations rather than their amplitude. Particle properties of light Wave properties of light ,ph ph E i p c r ,i k c ω r - both the time-like and space-like components of these 4-vectors should transform under L.Tr. in a similar way Thus, if Planck’s idea E=ħω is correct, than we must conclude that php k= rr h The phase is a Lorentz-invariant quantity, the (scalar) product of two 4-vectors: t krω − rr ( ),ict rr ,i k c ω⎛ ⎞ ⎜ ⎟ ⎝ ⎠ r t krω − rr ph hp k λ = =h Some numbers Visible light: λ = 0.4 – 0.8 micrometers violet red ( ) 8 19 34 7 19 3 10 / 5 106.62 10 3.1 4 10 1.6 10 /ph c m s JE violet h J s eV m eV Jλ − − − − × × = = × ⋅ = ≈ × × ( ) 1.6phE red eV≈ ( ) 34 14 27 8 6.6 10 7.5 10 1.65 10 3 10 /ph hf J s Hz kg mp violet c m s s − −× ⋅ × × ⋅= = = × × ( ) 8 14 7 3 10 7.5 10 4 10 mf violet Hz m− × = = × × ( ) 8 14 7 3 10 4.3 10 7 10 mf red Hz m− × = = × × ( ) 31 19 253.1 2 2 9.1 10 3.1 1.6 10 / 9.5 10e e kg mp K eV m K kg eV eV J s − − − ⋅= = = × × × × × = × for comparison, the momentum of an electron with K=3.1eV: more than two orders of magnitude greater than for a photon with this energy! Photoelectric Effect Historical Note: The photoelectric effect was accidentally discovered by Heinrich Hertz in 1887 during the course of the experiment that discovered radio waves. Hertz died (at age 36) before the first Nobel Prize was awarded. Observation: when a negatively charged body was illuminated with UV light, its charge was diminished. J.J. Thomson and P. Lenard determined the ration e/m for the particles emitted by the body under illumination – the same as for electrons. The effect remained unexplained until 1905 when Albert Einstein postulated the existence of quanta of light -- photons -- which, when absorbed by an electron near the surface of a material, could give the electron enough energy to escape from the material. Robert Milliken carried out a careful set of experiments, extending over ten years, that verified the predictions of Einstein’s photon theory of light. Einstein was awarded the 1921 Nobel Prize in physics: "For his services to Theoretical Physics, and especially for his discovery of the law of the photoelectric effect." Milliken received the Prize in 1923 for his work on the elementary charge of electricity (the oil drop experiment) and on the photoelectric effect. Photon-based explanation of Ph. E. Absorption of a photon by an electron in metal (inelastic collision between these particles) energy conservation 2 2 e ph em c E m cγ + =the rest RF of an electron after the collision 1 0phEγ = = before after 2 em c K+ 2 em chf However, we’ve concluded that a free electron cannot absorb a photon! before after 2 em c K+ 2 em chf What’s wrong? The electron is not “free”, it is embedded in metal, and the chunk of metal is the second body that participates in the collision 2 2 2 2 ph e met e e met metE m c M c m c K M c K+ + = + + + momentum conservationph e metp p p= + r r r met eM m>>> Thus, while the electron is still inside metal ~ph e metp p p<< ~ e met e met mv v M 2 ~ 2 met e e met e e e met met M m mK v K K M M ⎛ ⎞ = <<<⎜ ⎟ ⎝ ⎠ energy conservationph eE K= momentum conservation The photon energy is absorbed by an electron (the energy absorbed by metal is negligibly small), but the momentum exchange between electron and metal is crucial for momentum conservation. (see Slide 6) ph e metp p p= + r r r Photon-based explanation of Ph. E. (cont’d) In the experiment, the electron is observed outside the metal. It takes some energy to escape: (consider an attraction between an electron and the positive “image” charge induced on the metal surface) metal q-q+ The “escape” energy: the work function W (material-specific) Thus, for the electron outside metal e ph K E W= − ( )eK f hf W= − 00eK hf W= → =“red” boundary of Ph. E. ( ) ( )0eK f h f f= − 0f Planck’s constant measurements: ( ) ( )0 0 0 eK f eV fh f f f f = = − − W− Photon-based explanation of Ph. E. (cont’d) e phK E W= − ( )eK f phE hf= W metal vacuum E Observations: For a given material of the cathode, the “stopping” voltage does not depend on the light intensity – the energy of photons is determined by the light frequency, not intensity The saturation current is proportional to the intensity of light at f =const – the saturation current is proportional to the number of photons, thus to the light intensity Material-specific “red boundary” f0 exists: no photocurrent at f < f0 – at f < f0 (hf < W) the photon energy is insufficient to extract an electron from metal Practically instantaneous response – no delay between the light pulse and the photocurrent pulse – single act of e-ph collision energy of a free electron in vacuum with Ke =0