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How did Planck come up with 'h'?

  1. Dec 4, 2008 #1
    In my new found passion to understand the "inner meaning" of this thing called quantum theory, I've been trying to find Planck's derivation of -- or explanation for choosing -- the "constant of nature" that has become so popular.

    I expected to be able to find the empirical basis for it very easily on google, but all I could find were explanations like, "a photon is a unit of radiation whose energy content can be found by E=hv." Well, this doesn't help me too much.

    The closest thing I have been able to find to an "explanation" is from this article...

    http://physicsworld.com/cws/article/print/373

    What's the reason for using this precise value?
     
    Last edited by a moderator: Apr 24, 2017
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  3. Dec 4, 2008 #2

    mgb_phys

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    You can measure it experimentally.
    You use a vacuum tube and excite electrons from the cathode with a light source of known wavelength and measure the voltage accross the tube.
    You can then get h/e from the slope - without having to know the work function of the cathode. If you know e you can get h.
     
  4. Dec 4, 2008 #3

    epenguin

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    It fitted an equation to experimental data, in his case of dependence of intensity of radiation on frequency for black body, that was the start of it all.
     
  5. Dec 4, 2008 #4
    Thanks. Can you point me in a direction where someone has actually done this? I'm looking for experimental details...
     
  6. Dec 4, 2008 #5

    mgb_phys

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    Milikan did it originally in 1916 but you still have to pay for access to the paper !
    http://focus.aps.org/story/v3/st23
    There are lots of ugrad lab classes on the web describing it.
     
  7. Dec 4, 2008 #6

    epenguin

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    These are the first things in any textbook that goes beyond classical or elementary physics - as the fact of my knowing them proves. :smile:
     
  8. Dec 4, 2008 #7

    mgb_phys

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    It's also quite an easy experiment to do nowadays with LEDs and vacuum tubes.
    Unlike Milikan's other experiments - it actualy works!
     
  9. Dec 4, 2008 #8
    Thanks for the heads up on Milikan. However, the question still remains: What was Planck's justification for using it in 1900? I mean, how did the inventor of h derive it?
     
  10. Dec 4, 2008 #9

    mgb_phys

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    Sorry - Planck didn't measure it, and apparently didn't really believe in it!
    He just realised mathemtically that if you made energy changes only available in discrete lumps it solved some problems in thermodynamics. Einstein used the idea to explain the photoelectric effect - so it's really as much Einstein's constant as Planck's.

    Sometimes it takes centuries for the experiment to measure a constant proposed by a theory - it took a long time for the speed of light and the gravitational constant G to be measured accurately.
     
  11. Dec 4, 2008 #10

    jtbell

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    Planck came up with the idea of quantized radiation and the constant we know as h, in deriving a formula to fit the observed spectrum from a hot "black body." The details are covered in many introductory modern physics textbooks, e.g. Beiser, "Concepts of Modern Physics", section 2.2; Krane, "Modern Physics", section 3.3; Ohanian, "Modern Physics", section 3.1.

    You might find these details on line by Googling for "black body radiation" or "blackbody radiation" or "Planck radiation formula".
     
  12. Dec 4, 2008 #11
    So, where in the heck did it come from? Did manna from heaven fall into his lap?:smile:


    Why did he pick these precise discrete lumps that now seem to fit so perfectly with empirical observation? Are you saying that the mathematics just "manifested it"?
     
  13. Dec 4, 2008 #12
    I don't think that a constant is the reason why the Rayleigh-Jeans Law was a failure. Wein's displacement law is the thing that corrected it, and it had nothing to do with a simple constant.
     
  14. Dec 4, 2008 #13

    mgb_phys

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    No he came up with the idea that if you only allow energy to transfer in small lumps then some problems in thermodynamics are solved. He didn't need to know what value h had - just that it was very small.
    It's the same as Newton's law of gravity - he knew that if the gravitational force was proportional the product of the masses and the distance squared then the orbits of planets worked out. It wasn't until a 100years later that Cavendish worked out what the value of 'G' was.
     
  15. Dec 4, 2008 #14
    Planck, in 1900 used: 6.55 x 10-34 J s
    (source in first post)

    The NIST standard, in 2008 says: 6.62606896 x 10-34 J s
    (source:http://physics.nist.gov/cgi-bin/cuu/Value?h)

    I'm assuming this is just a lucky guess?
     
  16. Dec 4, 2008 #15
  17. Dec 4, 2008 #16

    mgb_phys

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    Interesting - I hadn't realisied Planck had actually got a value
    You can derive it quite easily from Wien's law, which tells you frequency of the peak on the curve predicted by Planck's equation - of course this relies on you having a good value for Wien's constant!

    Planck's original paper (translated!) http://dbhs.wvusd.k12.ca.us/webdocs/Chem-History/Planck-1901/Planck-1901.html [Broken]
     
    Last edited by a moderator: May 3, 2017
  18. Dec 4, 2008 #17
    Yes... this is all very interesting, indeed. I'm doing my best to trace this thing back in history. My guess that Boltzmann is going to end up being known as the "real" father of QM!
     
  19. Dec 4, 2008 #18
    Post # 3 is as close as you'll get:

    http://en.wikipedia.org/wiki/Wien_displacement_law
     
  20. Dec 4, 2008 #19
    I'm sitting here reading Kuhn's "Black Body Theory and the Quantum Discontinuity 1894-1912". This is an extremely in depth look into the origins of QM.

    The first mention of the "b" constant that eventually becomes Planck's "h" is mentioned here:
    The internal quote from Planck is footnoted as: "Funfte Mittheilung" (Planck, 1899), p. 465; I, 585.

    Hello, thermodynamics! The plot thickens...
     
  21. Dec 4, 2008 #20
    Oh yeah? I'm reading a source of a source of a Wikipedia article!
     
  22. Dec 4, 2008 #21
    In p. 104 of Kuhn's book, already cited:

    From what I understand of Kuhn's argument, Planck's use of Boltzmann's combinatorial method as applied to Wein's empirically correct law is the thing that got this whole "integer only energy quanta" thing off the ground...
     
  23. Dec 4, 2008 #22
    Okay, this is what I've been looking for. h (Planck's) is nothing other that k (Boltzmann's). k is simply the gas constant (8.314472 J/K mol) divided by the Avogadro constant (6.02214179 entities per mol). There is apparently a controversy about who deserves credit for "discovering" this thing. According to http://en.wikipedia.org/wiki/Boltzmann_constant#Historical_note, Planck wrote in his Nobel Prize lecture:

    It seems as though Planck was positively obsessed with proving the laws of thermodynamics on the "micro" rather than on the "statistical" level; the latter is all that concerned Boltzmann. According to Kuhn, Planck did quite a lot of "mathematical fudging," and his proofs did not impress too many of his peer reviewers in the time around December 1900.

    But the "atomists" were ready and waiting to jump on anything that would bring Maxwell's continuous energy relations into a discrete form. So, when Einstein came along and popularized h in his own work, the physics world was primed for one heck of a party over the next few decades.
     
  24. Dec 4, 2008 #23

    jtbell

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    No. Planck's constant and Boltzmann's constant are two different things. They even have different units.
     
  25. Dec 4, 2008 #24

    marcus

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    http://www.knowledgerush.com/kr/encyclopedia/Planck_time/
    ==quote==

    Max Planck's creation of the natural units

    Max Planck first listed his set of units (and gave values for them remarkably close to those used today) in May of 1899 in a paper presented to the Prussian Academy of Sciences. Max Planck: 'Über irreversible Strahlungsvorgänge'. Sitzungsberichte der Preußischen Akademie der Wissenschaften, vol. 5, p. 479 (1899). At the time he presented the units, quantum mechanics had not been invented. He himself had not yet discovered the theory of blackbody radiation (first published December 1900) in which the constant h made its first appearance and for which Planck was later awarded the Nobel prize. The relevant parts of Planck's 1899 paper leave some confusion as to how he managed to come up with the units of time, length, mass, temperature etc. which today we define using h-bar and motivate by references to quantum physics before things like h-bar and quantum physics were known. Here's a quote from the 1899 paper that gives an idea of how Planck thought about the set of units.

    ...ihre Bedeutung für alle Zeiten und für alle, auch ausserirdische und ausser menschliche Culturen nothwendig behalten und welche daher als 'natürliche Maasseinheiten' bezeichnet werden können...

    ...These necessarily retain their meaning for all times and for all civilizations, even extraterrestrial and non-human ones, and can therefore be designated as 'natural units'...
    ==endquote==

    I've seen the German text of the 1899 article and I have an English translation somewhere. He gives a value for h that is very close to the right one, but it is hard to see how he came by it. He found it before the black body radiation law.

    The title of the 1899 paper is "On irreversible radiation processes". If I remember right, he delivered it sometime late spring or early summer to the Prussian Academy of Sciences in Berlin.

    Maybe googling the title would come up with an online copy.
     
    Last edited by a moderator: Apr 24, 2017
  26. Jan 6, 2009 #25
    This 46 page article looks promising - I haven't read it yet:

    Planck, the Quantum, and the Historians
    Clayton A. Gearhart Phys. perspect. 4 (2002) 170–215
    http://employees.csbsju.edu/cgearhart/pubs/PQH.pdf

    Translations to accompany it:

    http://employees.csbsju.edu/cgearhart/Planck/planck_1906.pdf

    This contains detailed discussion of how Planck developed his blackbody formula, in particular concerning how he approached entropy.

    I found this as one of a bunch of interesting looking papers at:

    http://enjoy.phy.ntnu.edu.tw/course/view.php?id=120#section2

    Also, perhaps (if one could get the text):

    The Historians' Disagreements over the Meaning of Planck's Quantum
    Darrigol, O Centaurus, Volume 43, Numbers 3-4, 1 December 2001 , pp. 219-239(21)
    http://www.ingentaconnect.com/content/mksg/cnt/2001/00000043/F0020003/art00044

    and

    "Max Planck and black-body radiation," essay in Dieter Hoffmann, ed., Max Planck:
    Annalen Papers (Wiley-VCH (2008), 395¬–414).
    http://employees.csbsju.edu/cgearhart/pubs/sel_pubs.htm

    - Robin
     
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