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Modern Physics modern physics physics 112N the quantum revolution ➜ all the physics I’ve shown you so far is “deterministic” ➜ if you precisely measure the condition of a system at some point in time ➜ and you know the “equations of motion” ➜ you can predict what will happen for evermore ➜ the “clockwork” universe for example - projectile motion - planets orbiting the sun - electric and magnetic fields from charges and currents ➜ physics was viewed this way until the turn of the 20th century ➜ when some simple experiments forced us to rethink our views physics 112N 2 the quantum revolution ➜ we now think of fundamental physics as “probabilistic” ➜ we can only calculate the relative odds of any particular event occurring (at least at microscopic scales) physics 112N 3 the quantum revolution ➜ we now think of fundamental physics as “probabilistic” ➜ we can only calculate the relative odds of any particular event occurring (at least at microscopic scales) ➜ e.g. in classical electromagnetism : electron electron hits here heavy + positive charge if we measure the position and velocity of the electron, we can use equations of motion to predict the exact path of the electron physics 112N 4 the quantum revolution ➜ we now think of fundamental physics as “probabilistic” ➜ we can only calculate the relative odds of any particular event occurring (at least at microscopic scales) ➜ e.g. in the quantum theory : electron lower probability high probability heavy + positive charge lower probability can only determine the relative probability that the electron will hit at each place on the wall physics 112N 5 the quantum revolution ➜ we now think of fundamental physics as “probabilistic” ➜ we can only calculate the relative odds of any particular event occurring (at least at microscopic scales) ➜ and yet our probabilistic theories are still incredibly precise the “anomalous magnetic moment” of the electron can be predicted by quantum theory and measured in experiment these two numbers agree to ten significant figures physics 112N 6 the quantum revolution ➜ how did we come to this ? ➜ TRYING TO EXPLAIN EXPERIMENTAL RESULTS ! the scientific method ➜ one of the first ‘troubling’ results was the ‘photoelectric effect’ physics 112N 7 the photoelectric effect ➜ a simple experimental observation ➜ shine UV light onto a charged electroscope and it discharges ➜ OK, interesting, let’s do a controlled experiment, varying properties of the light and the metal and see what happens physics 112N 8 the photoelectric effect ➜ experimental observations: 1. the current flowing increases in proportion to the intensity of the light 2. the current appears without time delay when the light is switched on 3. current only flows for light with frequency above some threshold, f > f0 4. the value of the threshold frequency f0 depends on the metal the cathode is made from 5. reversing and increasing the potential, the current flow can be stopped, and the potential required, -Vstop, is independent of the light intensity physics 112N 9 the photoelectric effect 3. current only flows for light with frequency above some threshold, f > f0 physics 112N 10 the photoelectric effect 5. reversing and increasing the potential, the current flow can be stopped, and the potential required, -Vstop, is independent of the light intensity physics 112N 12 the photoelectric effect applied voltage dependence when ΔV = -Vstop even the fastest electrons don’t make it ⇒ no current physics 112N 13 the photoelectric effect explain by conservation of energy the light provides energy to the electrons it ‘costs’ a certain amount of energy to pull the electron out of the metal whatever is left over goes into kinetic energy of the freed electron maybe the ‘cost’ can vary depending how ‘deep’ the electron is in the metal but there is a minimum cost and hence a maximum K.E. then ΔV = -Vstop corresponds to the energy needed to stop Kmax physics 112N 14 the photoelectric effect so what’s the problem ? 2. the current appears without time delay when the light is switched on 3. current only flows for light with frequency above some threshold, f > f0 our wave theory of electromagnetism says that energy arrives continuously, with more energy arriving for more intense light the frequency should be irrelevant ! physics 112N 15 the photoelectric effect the solution : light arrives not as a continuous wave, but in packets of energy, or quanta, now called photons the energy of each photon is given by where f is the frequency of the light and h is a universal constant Planck’s constant higher frequency light is made of particles which each have higher energy physics 112N 16 the photoelectric effect the solution : if the frequency of the light is too low, a single photon doesn’t have enough energy to overcome the work function physics 112N 17 light is particles now ? really ? sorry, but yes ... consider a double slit experiment performed with light of very low intensity some aspects of light are wave-like e.g. interference pattern and some are particle-like e.g. the individual arrival don’t like this ? it’s going to get worse ! physics 112N 19 light is particles now ? really ? but we don’t “see” individual light particles ! let’s crudely estimate the photon rate from a lightbulb: say the bulb emits 50 W of light energy 50 W = 50 J/s typical optical light wavelength = 500 nm energy of one photon number of photons emitted in one second a huge number, no wonder we don’t notice the individual particles physics 112N 20 ‘lumpy’ energy ➜ there are other experiments that suggest energy can come in discrete amounts ➜ atomic spectroscopy ➜ diffraction grating spectrometer physics 112N 21 atomic spectroscopy ➜ diffraction grating spectrometer results continuous spectrum - all colors discrete spectra - only certain special wavelengths only certain photon energies are emitted by ‘excited’ atoms physics 112N 22 energy of an atom ➜ can also do ‘absorption’ experiments - shine white light through a gas and put the resulting light through a diffraction grating a few discrete lines many more discrete lines physics 112N 23 energy conservation ➜ propose an atom can emit or absorb a photon emission + ‘excited’ atom less ‘excited’ atom photon energy conservation absorption + less ‘excited’ atom photon ‘excited’ atom energy conservation physics 112N 24 discrete atomic energies ➜ the emission and absorption spectra can be described assuming only certain discrete energies are allowed e.g. a hypothetical atom lowest allowed energy three six emission lines “ground state” absorption physics 112N lines 25 discrete atomic energies ➜ it is useful to know that the typical energy scale for atomic levels is electron-Volts e.g. ΔE ~ 2 eV photon ➜ visible light from atomic transitions ! chemistry is physics at scales measured in eV physics 112N 26 atomic energy levels from spectra ➜ suppose we measured the following visible absorption and emission spectra from a particular atom ➜ if the atom has only four energy levels, can we determine their energies ? physics 112N 27 atomic energy levels from spectra absorption ⇒ starting from ground state physics 112N 28 atomic energy levels from spectra emission ⇒ between any two levels physics 112N 29 atomic energy levels from spectra would also appear ✗ in absorption emission ⇒ between any two levels physics 112N 30 atomic energy levels from spectra emission ⇒ between any two levels physics 112N 31 atomic energy levels from spectra ✗not seen in emission emission ⇒ between any two levels physics 112N 32 atomic energy levels from spectra physics 112N 33 atomic energy levels from spectra physics 112N 34 atomic energy levels from spectra physics 112N 35 hydrogen energy level spectrum physics 112N 36 what’s going on inside the atom ? ➜ we think that atoms contain ➜ negatively charged light electrons in equal numbers to ensure ➜ positively charged heavy protons atoms are overall uncharged ➜ but how are they distributed ? ➜ J.J. Thomson who discovered the electron thought the charges were evenly distributed throughout the atom physics 112N 37 what’s going on inside the atom ? ➜ need more experimental results ... Rutherford, Geiger and Marsden ➜ bounce (‘scatter’) alpha particles off atoms - watch where they go physics 112N 38 Rutherford scattering & the atomic nucleus ➜ some of the alpha particles get scattered back toward the source ➜ protons tightly bound in a tiny atomic nucleus ➜ electrons much further out physics 112N 39 the planetary model of the atom ➜ consider the simplest atom : hydrogen - one electron and one proton ➜ classical electromagnetism - Coulomb’s law ➜ circular motion of the electron around the nucleus ? e- ➜ but any energy is possible in this model ➜ disagrees with the spectroscopy experiments p+ ➜ accelerating charges radiate e/m waves in classical electromagnetism ➜ continuous loss of energy ➜ atoms aren’t stable in this model physics 112N 40 investigating electrons ➜ maybe we need a better theory of electrons and other ‘matter’ particles before trying to understand atoms ➜ back to the two-slit experiment physics 112N 41 two slits with particles - bullets ➜ machine gun spraying bullets at two slits tin plate - dents when hit and makes a sound ⓵ ⓶ physics 112N 42 two slits with particles - bullets ➜ machine gun spraying bullets at two slits distribution through hole 1 ⓵ ⓶ distribution through hole 2 ➜ bullets arrive one at a time - particles ! physics 112N 43 two slits with particles - bullets ➜ machine gun spraying bullets at two slits distribution through hole 1 ⓵ total bullet distribution ⓶ distribution through
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