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4. Matter waves 27 electrons 70 electrons 735 electrons by 1920 shortcomings of Bohr’s model - can not explain intensity of spectral lines - limited success for multi electron systems but crucial to Bohr’s model are integer numbers (n), and integers otherwise in physics only in wave phenomena such as interference back to light: E = h f, so photons are energy, E = mc2, so photons are “kind of matter” although mass less, light is a wave, c = f Einstein 1906: p = E/c = h f/c must also be = h/ (we used this to explain Compton effect) de Broglie 1923 PhD thesis speculation; because photons have wave and particle characteristics, perhaps all forms of matter, e.g. electron, have wave as well as particle properties, p = h / for all particles, f = E / h , = h /p If that turns out to be true, I’ll quit physics, Max von Laue, Noble Laureate 1914, author of “Materiewelleninterferenzen” the classical text on electron diffraction (what if p = m v = 0 because particle is not moving, v = 0, h is a constant, so must be infinite – can’t be), consequence particles can never be truly at rest, v and p can be very very very low, but never zero!!!!! that is what is actually observed: a tiny tiny pendulum will be hit by air molecules and move all the time somewhat irregularly, a large pendulum will obey classical physics in other words: electrons and everything else also has a dual particle-wave character, an electron is accompanied by a wave (not an electromagnetic wave!!!) which guides/pilots the electron through space first great idea that let to acceptance of de Broglie hypothesis: the orbits of the electron in the Bohr model are of just the right size for standing waves (with multiples of wavelength ) to occur, a standing wave is a stationary state and so are the atomic orbits 2π r = n with r radius of electron orbit inserting n can be even or odd but has to be an integer = h/p = (from Einstein’s relativistic mechan