Tài liệu Chapter XX Quantum theory of light pdf

GENERAL PHYSICS III GENERAL PHYSICS III Optics & Quantum Physics Chapter XX Chapter XX Quantum theory of light Quantum theory of light §1. Blackbody radiation. Planck’s theory of radiation §2. Photoelectric effect. Einstein’s theory of light §3. Compton scattering  At the end of the 19-th century, physics was at its most confidence situation. Classical phyics, as formulated in Newton’s law of mechanics and Maxwell’s theory of electromagnetism, have proved very successful in solving every problem. → At that time there seemed to be no question for which physics co uld not provide an answer !!!  But then it came as a great shock when some simple phenomena were observed which could not be explained by classical physics → a new theory, quantum theory, was developed at the beginning of the 20-th century  We begin our study of quantum physics by two following phenomena: • Blackbody radiation • Photoelectric effect We will see what were the failures of classical physics and how a new theory had been developed. §1. Blackbody radiation. Planck’s theory of radiation: • Heat bodies emit electromagnetic radiation in the infra-red region of the spectrum (see the next slide). In this region the radiation is not visible. • As the temperature of a body is increased to any value, the body begins to glow red and then white, emitting visible electromagnetic radiation. (an example is the variation of the radiation of a filament of electric lamp when the electric current varies). • Observation of the spectrum emitted by a solid shows that the radiation extends over a continous range of frequency. Such a spectrum is called a continuum. 1.1 Experimental laws of blackbody radiation: 1.1.1 Stephan-Boltzmann law: • It was observed that the intensity of the radiation emitted from a body increases rapidly with increasing temperature of the body. [...]... emitted in the form of energy quanta, each quantum is h  Planck’s theory gave the consequences that agree well with the experimental laws for the blackbody radiation Planck’s hypothesis is recognised as the beginning of a new theory, the quantum theory • In 1905 Einstein developed an analogue theory for light: Light consists of photons, the energy of each photon is h  Einstein’s theory gave a satisfactory... Einstein introduced the quantum theory of light, and developed the correct analysis of the photoelectric effect in 1905 2.2.1 Einstein’s postulates: By analogy to the earlier Planck’s theory of radiation, the postulates of Einstein’s theory is as follows:  Light consists of small “packages” of energy called photons or light quanta  The energy  a photon is  h  of =   where h is the Plank constant... any light with     This results are hard to understand on the basis of classical physics ! (According to classical physics: if the light intensity increases, electrons gain more energy → have more chance to escape Don’t understand why is there a limit frequency  )  2.2 Einstein’s quantum theory of light: To overcome the difficulty of classical physics, Albert Einstein introduced the quantum theory. .. phenomenon that provides additional direct confimation of the quantum nature of light, and particularly, of X-rays 3.1 Experimental results: • The wavelength of the incoming monochromatic X-rays:  • The wavelength of the scattering X-rays:  ’ Experimental observations discovered a shift in wavelength:  ≠ (A.H Compton 1923) ’ The wavelength shift of scattered X-rays is called the Compton effect • It... with the incident X-rays ) The Compton effect could not be interpreted by classical physics !! But on the basis of the photon model of light one has a satisfactory explanation of this effect 3.2 Compton effect as the result of photon-electron collision: On the basis of the photon model of light, we consider the Compton scattering as the following collision process + e →  + e’ ’  and e - photon and... The discrete nature of energy is the foundation of quantum theory One more remark: The large wavelength limit of the Planck’s spectrum formula is the Rayleigh’s formula (recall e x ≈1 + x with small x) This means that at very long wavelengths (very small quanta energies), quantum effects become unimportant §2.Photoelectric effect Einstein’s theory of light: 2.1 Photoelectric effect:  Consider a metal... interpretation of the experimental results of the photoeffect, which could not explained by classical physics  In 1923 Compton observed the wavelength shift of scattered X-rays This effect was interpreted excelently by the photon model of light The formula for the wavelength shift was derived by using the equations which express the conservation of the total energy and the total momentum of the collision of. .. showed the “particle” nature of electromagnetic waves (thermal radiation, visible light, X-rays,…) Electromagnetic waves can be considered as flows of photons • In the limit of large wavelengths (high frequencies, small photon energies) quantum effects become unimportant The “particle” behavior of electromagnetic waves is remarkable in short-wavelength regions of the continuum of electromagnetic waves...  the incident light ?  of Incident Light (variable frequency  )  Experiment 1: Measure the maximum energy of ejected electrons  Collector A electrons Metal Surface + vacuum V   The electric field between the “collector” and the metal will repel ejected electrons Increase negative voltage until flow of ejected electrons decreases to zero (Current = 0 at V = Vstop) Measurement of Vstop tells the... Analysis of the photoeffect by the quantum theory: A photon arriving at the surface is absorbed by an electron (one by one) After that the electron gets all the photon’s energy (h ) For an electron we can write the following equation: mv2 h   max  2 The energy of the electron after absoption of photon The energy part for escaping from the metal surface The remaining part, the kinetic energy of the . III Optics & Quantum Physics Chapter XX Chapter XX Quantum theory of light Quantum theory of light §1. Blackbody radiation. Planck’s theory of radiation §2   ). 2.2 Einstein’s quantum theory of light: To overcome the difficulty of classical physics, Albert Einstei n introduced the quantum theory of light, and developed