User:Johnjbarton/sandbox/introduction to quantum mechanics: Difference between revisions

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=== Evidence of quanta from the photoelectric effect ===

The seeds of the quantum revolution appear in the discovery by [[JJ Thomson]] in 1897 that [[cathode rays]] were actuallynot continuous but "corpuscles" oridentical particles now calledto [[electrons]]. SinceElectrons nohad solidbeen theorynamed ofjust cathodesix raysyears existed,as part of the electronemerging wastheory of [[atoms]]. excitingIn news1900, but[[Max notPlanck]], a revolution.conservative However,physicist inunconvinced 1905by Einsteinthe proposed[[atomic thattheory]], lightdiscovered wasthat alsohe corpuscular,needed consistingdiscrete ofentities "energylike quanta",atoms seeminglyor in contradictionelectrons to theexplain established[[blackbody scienceradiation]].<ref>{{Cite ofbook light|last=Baggott as|first=J. aE. continuous|title=The wave,quantum stretching backstory: a hundredhistory yearsin to40 [[Thomasmoments Young|date=2013 Young's]]|publisher=Oxford work on [[diffraction]]Univ. LightPress quanta|isbn=978-0-19-965597-7 would|edition=Impression: be3 revolutionary.|___location=Oxford}}</ref>

[[File:Black body.svg|thumb|upright=1.4|Blackbody radiation intensity vs color and temperature. The rainbow bar represents visible light; 5000K objects are "white hot" by mixing differing colors of visible light. To the right is the invisible infrared. Curves are predicted by quantum theories.]]

Einstein's evidence was twofold. First he analyzed [[blackbody radiation]]. Hot objects radiate heat; very hot objects – red hot, white hot objects – all look similar when heated to the same temperature. This temperature dependent "look" results from a common curve of light intensity at different frequencies (colors). The common curve is called blackbody radiation. The lowest frequencies are invisible heat rays – infrared light. White hot objects have intensity across many colors in the visible range. Continuous wave theories of light and matter cannot explain the blackbody radiation curve. Einstein showed that, by assuming that light energy transferred in discrete "energy quanta", the radiation curve could be explained. [[Max Planck]] showed the same result five years earlier, but he did not propose that the light was quantized.

[[File:Black body.svg|thumb|upright=1.4|Blackbody radiation intensity vs color and temperature. The rainbow bar represents visible light; 5000K objects are "white hot" by mixing differing colors of visible light. To the right is the invisible infrared. CurvesClassical theory (black curve for 5000K) fails; the other curves are correct predicted by quantum theories.]]

Einstein's second evidence connected to JJ Thomson's electron. In 1902, [[Philipp Lenard]] directed light from an arc lamp onto freshly cleaned metal plates housed in an evacuated glass tube. Then he measured the electric current coming off the metal plate, for higher and lower intensity of light and for different metals. This is the [[photoelectric effect]]. Lenard showed that amount of current – the number of electrons – depended on the intensity of the light, but that the velocity of these electrons did not depend on intensity.

Einstein's evidence was twofold. First he analyzed [[blackbody radiation]]. Hot objects radiate heat; very hot objects – red hot, white hot objects – all look similar when heated to the same temperature. This temperature dependent "look" results from a common curve of light intensity at different frequencies (colors). The common curve is called blackbody radiation. The lowest frequencies are invisible heat rays – infrared light. White hot objects have intensity across many colors in the visible range. Continuous wave theories of light and matter cannot explain the blackbody radiation curve. EinsteinPlanck showedspread that,the by assuming that lightheat energy transferredamong in discreteindividual "energy quantaoscillators", theof radiationan curveundefined couldcharacter bebut explained.with [[Maxdiscrete Planck]]energy showedcapacity: the sameblackbody resultradiation fivebehavior yearswas earlier,then but he did not propose that the light was quantizedcorrect.

At the time, electrons, atoms, and discrete oscillators were all exotic ideas to explain exotic phenomena. But in 1905 [[Albert Einstein]] proposed that light was also corpuscular, consisting of "energy quanta", seemingly in contradiction to the established science of light as a continuous wave, stretching back a hundred years to [[Thomas Young]]'s work on [[diffraction]].

The continuous wave theories of the time would predict that the electron would be accelerated to higher velocity if the light intensity was increased. Einstein's energy quanta explained the increase: one electron is ejected for each quanta: more quanta means more electrons.

His revolutionary proposal started by reanalyzing Planck blackbody theory, arriving at the same conclusions by using the new "energy quanta". Einstein's secondthen showed how energy evidencequanta connected to JJ Thomson's electron. In 1902, [[Philipp Lenard]] directed light from an arc lamp onto freshly cleaned metal plates housed in an evacuated glass tube. Then heHe measured the electric current coming off the metal plate, for higher and lower intensity of light and for different metals. This is the [[photoelectric effect]]. Lenard showed that amount of current – the number of electrons – depended on the intensity of the light, but that the velocity of these electrons did not depend on intensity. The continuous wave theories of the time would predict that more light intensity would accelerate the same amount of current to higher velocity contrary to experiment. Einstein's energy quanta explained the volume increase: one electron is ejected for each quanta: more quanta mean more electrons.

Einstein then predicted that the electron velocity would increase in direct proportion to the light frequency above a fixed value that depended upon the metal. Here the idea is that energy in energy-quanta depends upon the light frequency; the energy transferred to the electron comes in proportion to the light frequency. The type of metal gives a [[work function | barrier]], the fixed value, that the electrons must climb over to exit and be measured.

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| Experiment || current increase || energy increase

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| Continuous Theory || X energy increase || ?

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| Quantum Theory || ✔ current increase ✔|| ✔ energy increase ✔

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