Lecture VI ( Feb 7, 2018)

Transcription

1 Lecture VI ( Feb 7, 2018) I. BEFORE BEFORE EINSTEIN ARRIVES IN NEW YORK : Planck s theory: radiations from hot objects come in pockets of energy quanta and each quanta has energy E = hf. 1905: Einstein s theory that light consists of finite number of energy quanta where energy of each quantum E = hf. He proposes photoelectric effect to test his theory. 1913, Planck still does not believe in Einstein s theory and Einstein described Planck as stubborn, attached to old ideas that are false. 1913, Danish physicist Neil s Bohr proposes revolutionary ideas about structure of atom that supported Einstein s ideas. ( We will discuss Bohr s model later ) 1912: Robert Millikan visits Planck for six months, during his sabbatical year from university of Chicago. He and Planck discussed the radiation quanta and Planck emphasized his disagreement with Einstein s picture. 1915: Robert Millikan, American experimentalist confirms E = hf in his photoelectric experiments. However, he did not believe that Einstein s picture is right and he stated that clearly in his paper describing his experiments on photoelectric effect. Photoelectric experiments, although consistent with E = hf did not prove that radiation consisted of particles. If radiations consisted of particles, then experiments should demonstrate that each radiation quantum speeds through space in a specific direction and does not speak like waves as Maxwell s theory predicts Planck wins nobel prize in physics. 1919: Einstein s general theory of relativity was confirmed in experiments and Einstein becomes an international celebrity. Although every one though that he is thinking about his relativity theory, Einstein later wrote, I have thought a hundred times as much about quantum theory as I have about general theory of relativity. ( He received nobel prize in 1921 for his theory of light quanta. ) 1

2 II. COMPTON ENTERS... At Washington university in St Louis, Arthur Compton was studying scattering of radiations electrons. If radiations are like water waves, they will bounce of the electrons without changing their frequency. Compton found that frequency of the radiations changed, like blue light was transformed into red light: his experiments to see this change of frequency required x-rays as the shift in frequency was very small. After years of trying, he could not explain his results. In 1922, he realized that the key to the puzzle is that radiation quanta have momentum and the scattering of light by electrons is like scattering of two particles and after scattering the energy of each particle will change. So Compton experiment of scattering of light by electrons is microscopic version of scattering of two billiards. The interesting thing to note is that he was not aware of Einstein s theory of light quanta. Many doubted Compton s result. But repeated experiments finally brought the community 2

3 to the consensus that his results are correct and his discovery is a revolutionary change in our idea regarding electromagnetic radiations. In other words, Maxwell s theory of light is not the right theory to describe electromagnetic waves. FIG. 1: Formula for Compton scattering: λ λ = h m ec (1 cos θ). 3

4 III. FRENCH PHYSICIST: LOUIS DE BROGLIE - WAVE- PARTICLE DUALITY Majored in history in 1913 and then switched to physics as his brother Maurice De Broglie was an experimental physicist... After learning about Compton experiment, Louis De Broglie argued that if electromagnetic waves can behave like particles then particles like electrons can also behave like waves. A. Matter Waves or De Broglie Waves The following two equations describe the de-broglie hypothesis: λ = h p, f = E h (1) where p = mv (2) For photons, p = E/c. In applications where it is natural to use the angular frequency ω = 2πf (i.e. where the frequency is expressed in terms of radians per second instead of rotations per second or Hertz) it is often useful to write expressions in terms of reduced Planck constant which is the Planck constant divided by 2π, and is denoted as (pronounced h-bar ): = h 2π = (47) Joule sec (3) The constant is what lies at the heart of quantum science. Yes, it is a pretty small and that is why quantum effects are usually irrelevant in macroscopic world. Readers will notice the presence of explicitly in all equations providing quantum description of a particle. 4

5 B. Some Constants mass of the electron, m e = 9X billion. That means we will need electrons to weigh one kg, which is thousand billion, billion, mass of the proton, m p 2000 times the mass of electron Planck constant h = 6.63X10 34 Joule sec One Calorie is 4.2 Joules Unit of energy in diet is Kilo-Calorie 5