Xem mã nguồn của Định luật Planck

[[Tập tin:Black body.svg|thumb|right|300px|Định luật Planck (minh họa bằng các đường cong màu) miêu tả chính xác bức xạ vật đen và giải quyết vấn đề "thảm họa cực tím" (đường màu đen).]]

'''Định luật Planck''' miêu tả bức xạ điện từ phát ra từ [[vật đen]] trong trạng thái [[cân bằng nhiệt]] ở một [[nhiệt độ]] xác định. Định luật đặt tên theo [[Max Planck]], nhà vật lý đã nêu ra nó vào năm 1900. Định luật này là bước đi tiên phong đầu tiên của [[vật lý hiện đại]] và [[cơ học lượng tử]].

Đối với [[tần số]] {{math|''ν''}}, hoặc [[bước sóng]] {{math|''λ''}}, định luật Planck viết dưới dạng:
:<math>B_\nu(T) = \frac{ 2 \Pi.h \nu^3}{c^2} \frac{1}{e^\frac{h\nu}{k_\mathrm{B}T} - 1}</math>

hoặc

:<math>B_\lambda(T) =\frac{2 hc^2}{\lambda^5}\frac{1}{ e^{\frac{hc}{\lambda k_\mathrm{B}T}} - 1}</math>

trong đó {{math|''B''}} ký hiệu của cường độ bức xạ (spectral radiance), {{math|''T''}} là nhiệt độ tuyệt đối, {{math|''k''<sub>B</sub>}} là [[hằng số Boltzmann]], {{math|''h''}} là [[hằng số Planck]], và {{math|''c''}} là [[tốc độ ánh sáng]] trong môi trường hoặc trong chân không.<ref name="Planck 1914 6 168">{{harvnb|Planck|1914|pp=6,&nbsp;168}}</ref><ref name="Chan8">{{harvnb|Chandrasekhar|1960|p=8}}</ref><ref name="Rybicki 1979 22">{{harvnb|Rybicki|Lightman|1979|p=22}}</ref> Đơn vị SI của phương trình là {{nobreak|W·sr<sup>−1</sup>·m<sup>−2</sup>·Hz<sup>−1</sup>}} đối với {{math|''B''<sub>''ν''</sub>(''T'')}} và {{nobreak|W·sr<sup>−1</sup>·m<sup>−3</sup>}} đối với {{math|''B''<sub>''λ''</sub>(''T'')}}. Định luật này cũng có thể biểu diễn theo cách khác, như số lượng [[photon]] phát ra tại một bước sóng xác định, hoặc mật độ năng lượng trong thể tích chứa bức xạ. Trong giới hạn đối với những tần số nhỏ (hay bước sóng dài), định luật Planck tương đương với [[định Rayleigh–Jeans|định luật Rayleigh–Jeans]], trong khi đối với những tần số lớn (bước sóng nhỏ) định luật này tương đương với [[xấp xỉ Wien]] hoặc [[định luật dịch chuyển Wien]].

[[Max Planck]] đưa ra định luật vào năm 1900, với mục đích ban đầu để đo các hằng số bằng thực nghiệm, và sau đó ông chứng minh rằng, như định luật biểu diễn sự phân bố năng lượng, nó miêu tả duy nhất sự phân bố ổn định của bức xạ trong trạng thái cân bằng nhiệt.<ref name="Planck 1914 42">{{harvnb|Planck|1914|p=42}}</ref> Là định luật về sự phân bố năng lượng, nó là một trong các định luật về phân bố cân bằng nhiệt mà bao gồm [[phân bố Bose–Einstein]], [[phân bố Fermi–Dirac]] và [[phân bố Maxwell–Boltzmann]].

==Tham khảo==
{{tham khảo|colwidth=30em}}

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*{{chú thích sách
 |last1=Kuhn
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 |year=1978
 |title=Black–Body Theory and the Quantum Discontinuity
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 }}
*{{chú thích sách
 |last1=Landsberg
 |first1=P.T.
 |year=1961
 |title=Thermodynamics with Quantum Statistical Illustrations
 |url=https://archive.org/details/thermodynamicswi0002land
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 }}
*{{chú thích sách
 |last1=Landsberg |first1=P.T.
 |year=1978
 |title=Thermodynamics and Statistical Mechanics
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 }}
*{{chú thích tạp chí
 |last1=Lewis |first1=G. N.
 |author1-link=Gilbert N. Lewis
 |year=1926
 |title=The Conservation of Photons
 |journal=[[Nature (tạp chí)|Nature]]
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 }}
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 }}
*{{chú thích tạp chí
 |last1=Lowen |first1=A. N.
 |last2=Blanch |first2=G.
 |year=1940
 |title=Tables of Planck's radiation and photon functions
 |journal=Journal of the Optical Society of America
 |volume=30 |issue=2 |page=70
 |doi=10.1364/JOSA.30.000070
 }}
*{{chú thích tạp chí
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 |last2=Kurlbaum |first2=F.
 |year=1898
 |title=Der electrisch geglühte "absolut schwarze" Körper und seine Temperaturmessung
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 |volume=17
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 }}
*{{chú thích tạp chí
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 |last2=Pringsheim |first2=E.
 |year=1899
 |title=1. Die Vertheilung der Energie in Spectrum des schwarzen Körpers und des blanken Platins; 2. Temperaturbestimmung fester glühender Körper
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 |volume=1
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 }}
*{{chú thích tạp chí
 |last1=Lummer |first1=O.
 |last2=Kurlbaum |first2=F.
 |year=1901
 |title=Der elektrisch geglühte "schwarze" Körper
 |journal=Annalen der Physik
 |volume=310
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 |doi=10.1002/andp.19013100809
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 |last1=Mandel
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 |title=Optical Coherence and Quantum Optics
 |url=https://archive.org/details/opticalcoherence0000mand
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 |last1=Mehra |first1=J.
 |last2=Rechenberg |first2=H.
 |year=1982
 |title=The Historical Development of Quantum Theory
 |volume=1 |issue=1
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 }}
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 |last1=Messiah |first1=A.
 |others=Temmer, G. G. (transl.)
 |year=1958
 |title=Quantum Mechanics
 |publisher=John Wiley & Sons
 }}
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 |year=1888
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 |journal=Philosophical Magazine
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 |doi=10.1080/14786448808628207
}}
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 |year=1984
 |title=Foundations of Radiation Hydrodynamics
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 }}
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 |year=1930
 |title=Thermodynamics of the Stars
 |journal=Handbuch der Astrophysik
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 }}
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 |last1=Paltridge
 |first1=G. W.
 |last2=Platt
 |first2=C. M. R.
 |year=1976
 |title=Radiative Processes in Meteorology and Climatology
 |url=https://archive.org/details/radiativeprocess0000palt
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 }}
*{{chú thích tạp chí
 |last1=Paschen |first1=F.
 |year=1895
 |title=Über Gesetzmäßigkeiten in den Spectren fester Körper und über ein neue Bestimmung der Sonnentemperatur
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 |pages=294–304
 |bibcode=
 |doi=
 }}
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 |last1=Pauli |first1=W.
 |author1-link=Wolfgang Pauli
 |year=1973
 |editor-last=Enz |editor-first=C. P.
 |others=Margulies, S.; Lewis, H. R. (transl.)
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 }}
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 |last1=Planck |first1=M.
 |author1-link=Max Planck
 |year=1900a
 |title=Über eine Verbesserung der Wienschen Spektralgleichung
 |journal=Verhandlungen der Deutschen Physikalischen Gesellschaft
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 }} Translated in {{chú thích sách
 |last1=ter Haar
 |first1=D.
 |year=1967
 |chapter=On an Improvement of Wien's Equation for the Spectrum
 |url=http://www.ffn.ub.es/luisnavarro/nuevo_maletin/Planck%20%281900%29,%20Improvement%20of%20Wien%27s.pdf
 |title=The Old Quantum Theory
 |publisher=Pergamon Press
 |pages=79–81
 |lccn=66029628
 |access-date=2014-06-08
 |archive-date=2016-10-10
 |archive-url=https://web.archive.org/web/20161010010043/http://www.ffn.ub.es/luisnavarro/nuevo_maletin/Planck%20%281900%29,%20Improvement%20of%20Wien%27s.pdf
 }}
*{{chú thích tạp chí
 |last1=Planck |first1=M.
 |year=1900b
 |title=Zur Theorie des Gesetzes der Energieverteilung im Normalspektrum
 |journal=Verhandlungen der Deutschen Physikalischen Gesellschaft
 |volume=2 |page=237
 }} Translated in {{chú thích tạp chí
 |last1=ter Haar
 |first1=D.
 |year=1967
 |chapter=On the Theory of the Energy Distribution Law of the Normal Spectrum
 |url=http://www.ffn.ub.es/luisnavarro/nuevo_maletin/Planck%20%281900%29,%20Distribution%20Law.pdf
 |title=The Old Quantum Theory
 |publisher=Pergamon Press
 |page=82
 |lccn=66029628
 |access-date=2014-06-08
 |archive-date=2016-09-20
 |archive-url=https://web.archive.org/web/20160920053757/http://www.ffn.ub.es/luisnavarro/nuevo_maletin/Planck%20%281900%29,%20Distribution%20Law.pdf
 }}
*{{chú thích tạp chí
 |last1=Planck |first1=M.
 |year=1900c
 |title=Entropie und Temperatur strahlender Wärme
 |journal=Annalen der Physik
 |volume=306 |issue=4 |pages=719–737
 |bibcode=1900AnP...306..719P
 |doi=10.1002/andp.19003060410
 }}
*{{chú thích tạp chí
 |last1=Planck |first1=M.
 |year=1900d
 |title=Über irreversible Strahlungsvorgänge
 |journal=Annalen der Physik
 |volume=306
 |issue=1
 |pages=69–122
 |bibcode=1900AnP...306...69P
 |doi=10.1002/andp.19003060105
 }}
*{{chú thích tạp chí
 |last1=Planck
 |first1=M.
 |year=1901
 |title=Über das Gesetz der Energieverteilung im Normalspektrum
 |url=https://archive.org/details/sim_annalen-der-physik_1901_4_3/page/553
 |journal=Annalen der Physik
 |volume=4
 |page=553
 |doi=10.1002/andp.19013090310
 }} Translated in {{chú thích web
 |last1=Ando
 |first1=K.
 |year=
 |title=On the Law of Distribution of Energy in the Normal Spectrum
 |url=http://theochem.kuchem.kyoto-u.ac.jp/Ando/planck1901.pdf
 |access-date=ngày 13 tháng 10 năm 2011
 |archive-date=2015-02-22
 |archive-url=https://web.archive.org/web/20150222133544/http://theochem.kuchem.kyoto-u.ac.jp/Ando/planck1901.pdf
 }}
*{{chú thích sách
 |last1=Planck |first1=M.
 |year=1906
 |title=Vorlesungen über die Theorie der Wärmestrahlung
 |publisher=Johann Ambrosius Barth 
 |lccn=07004527
}}
*{{chú thích sách
 |last1=Planck
 |first1=M.
 |others=Masius, M. (transl.)
 |year=1914
 |title=The Theory of Heat Radiation
 |url=https://archive.org/details/theoryofheatradi0000plan
 |publisher=P. Blakiston's Son & Co.
 |edition=2
 |ol=7154661M
 }}
*{{chú thích sách
 |last1=Planck |first1=M.
 |others=Wills, A. P. (transl.)
 |year=1915
 |title=Eight Lectures on Theoretical Physics
 |publisher=Dover Publications
 |isbn=0-486-69730-4
 }}
*{{chú thích tạp chí
 |last1=Planck |first1=M.
 |year=1943
 |title=Zur Geschichte der Auffindung des physikalischen Wirkungsquantums
 |journal=Naturwissenschaften
 |volume=31 |issue=14–15 |pages=153–159
 |bibcode=1943NW.....31..153P
 |doi=10.1007/BF01475738
 }}
*{{chú thích tạp chí
 |last1=Rayleigh |first1=Lord
 |year=1900
 |title=LIII. Remarks upon the law of complete radiation
 |journal=Philosophical Magazine
 |series=Series 5 |volume=49 |issue=301 |page=539
 |doi=10.1080/14786440009463878
 }}
*{{chú thích tạp chí
 |last1=Rayleigh |first1=Lord
 |year=1905
 |title=The Dynamical Theory of Gases and of Radiation
 |journal=Nature (journal)
 |volume=72 |issue=1855 |pages=54–55
 |bibcode=1905Natur..72...54R
 |doi=10.1038/072054c0
 }}
*{{chú thích sách
 |last1=Razavy |first1=M.
 |year=2011
 |title=Heisenberg's Quantum Mechanics
 |publisher=World Scientific
 |isbn=978-981-4304-10-8
 }}
*{{chú thích tạp chí
 |last1=Rubens |first1=H.
 |last2=Kurlbaum |first2=F.
 |year=1900a
 |title=Über die Emission langer Wellen durch den schwarzen Körper
 |journal=Verhandlungen der Deutschen Physikalischen Gesellschaft
 |volume=2 |page=18
 }}
*{{chú thích tạp chí
 |last1=Rubens |first1=H.
 |last2=Kurlbaum |first2=F.
 |year=1900b
 |title=Über die Emission langwelliger Wärmestrahlen durch den schwarzen Körper bei verschiedenen Temperaturen
 |journal=Sitzungsberichte der Königlich Preussischen Akademie der Wissenschaften zu Berlin
 |pages=929–941
 }} Translated in {{chú thích tạp chí
 |last1=Rubens
 |first1=H.
 |last2=Kurlbaum
 |first2=F.
 |year=1901
 |title=On the heat-radiation of long wave-length emitted by black bodies at different temperatures
 |url=https://archive.org/details/sim_astrophysical-journal_1901-12_14_5/page/335
 |journal=The Astrophysical Journal
 |volume=14
 |pages=335–348
 |bibcode=1901ApJ....14..335R
 |doi=10.1086/140874
 }}
*{{chú thích sách
 |last1=Rybicki
 |first1=G. B.
 |last2=Lightman
 |first2=A. P.
 |year=1979
 |title=Radiative Processes in Astrophysics
 |url=http://books.google.com/books?id=LtdEjNABMlsC&printsec=frontcover
 |publisher=John Wiley & Sons
 |isbn=0-471-82759-2
 }}
*{{chú thích sách
 |last1=Sharkov
 |first1=E. A.
 |year=2003
 |chapter=Black-body radiation
 |title=Passive Microwave Remote Sensing of the Earth
 |url=http://www.iki.rssi.ru/asp/pub_sha1/Sharch06.pdf
 |publisher=Springer (publisher)
 |isbn=978-3-540-43946-2
 }}
*{{chú thích sách
 |last1=Schiff
 |first1=L. I.
 |year=1949
 |title=Quantum Mechanics
 |url=https://archive.org/details/quantummechanics0000leon_g7q0
 |publisher=McGraw-Hill
 }}
*{{chú thích sách
 |last1=Schirrmacher |first1=A.
 |year=2001
 |title=Experimenting theory: the proofs of Kirchhoff's radiation law before and after Planck
 |publisher=Münchner Zentrum für Wissenschafts und Technikgeschichte
 }}
*{{chú thích sách
 |last1=Schumm
 |first1=B. A.
 |year=2004
 |title=Deep down things: the breathtaking beauty of particle physics
 |url=http://books.google.ca/books?id=htJbAf7xA_oC
 |publisher=Johns Hopkins University Press
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 }}
*{{chú thích sách
 |last1=Schwinger |first1=J.
 |author1-link=Julian Schwinger
 |year=2001
 |chatper=
 |editor-last=Englert |editor-first=B.-G.
 |title=Quantum Mechanics: Symbolism of Atomic Measurements
 |url=https://archive.org/details/quantummechanics0000schw_w7l9 |publisher=Springer (publisher) |isbn=3-540-41408-8
 }}
*{{chú thích sách
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 |last2=Zubairy |first2=M.S.
 |author2-link=Muhammad Suhail Zubairy
 |year=1997
 |title=Quantum Optics
 |publisher=Cambridge University Press
 |isbn=0-521-43458-0
 }}
*{{chú thích tạp chí
 |last1=Siegel
 |first1=D.M.
 |year=1976
 |title=Balfour Stewart and Gustav Robert Kirchhoff: two independent approaches to "Kirchhoff's radiation law"
 |url=https://archive.org/details/sim_isis_1976-12_67_239/page/565
 |journal=Isis
 |volume=67
 |pages=565–600
 |doi=10.1086/351669
 }}
*{{chú thích sách
 |last1=Siegel
 |first1=R.
 |last2=Howell
 |first2=J. R.
 |year=2002
 |title=Thermal Radiation Heat Transfer, Volume 1
 |url=http://books.google.com/books?id=O389yQ0-fecC&pg=PA25#v=onepage&q&f=false
 |edition=4
 |publisher=Taylor & Francis
 |isbn=978-1-56032-839-1
 }}
*{{chú thích sách
 |last1=Sommerfeld
 |first1=A.
 |others=Brose, H. L. (transl.)
 |author1-link=Arnold Sommerfeld
 |year=1923
 |title=Atomic Structure and Spectral Lines
 |url=http://books.google.com/books/about/Atomic_structure_and_spectral_lines.html?id=u1UmAAAAMAAJ
 |edition=3
 |publisher=Methuen Publishing
 }}
*{{chú thích sách
 |last1=Stehle |first1=P.
 |year=1994
 |title=Order, Chaos, Order. The Transition from Classical to Quantum Physics
 |publisher=Oxford University Press
 |isbn=0-19-507513-7
 }}
*{{chú thích tạp chí
 |last1=Stewart |first1=B.
 |year=1858
 |title=An account of some experiments on radiant heat
 |journal=Transactions of the Royal Society of Edinburgh
 |volume=22 |pages=1–20
 |doi=
 }}
*{{chú thích sách
 |last1=ter Haar
 |first1=D.
 |year=1967
 |title=The Old Quantum Theory
 |url=https://archive.org/details/oldquantumtheory00haar
 |publisher=Pergamon Press
 |lccn=66-029628
 }}
*{{chú thích sách
 |last1=Thornton |first1=S. T.
 |last2=Rex |first2=A. F.
 |year=2002
 |title=Modern Physics
 |publisher=Thomson Learning
 |isbn=0-03-006049-4
 }}
*{{chú thích sách
 |last1=Tisza |first1=L.
 |year=1966
 |title=Generalized Thermodynamics
 |publisher=MIT Press
 }}
*{{chú thích tạp chí
 |last1=Tyndall |first1=J.
 |author1-link=John Tyndall
 |year=1865a
 |title=Über leuchtende und dunkle Strahlung
 |journal=Annalen der Physik und Chemie
 |volume=200
 |pages=36–53
 |doi= 10.1002/andp.18652000103
 |bibcode = 1865AnP...200...36T }}
*{{chú thích sách
 |last1=Tyndall
 |first1=J.
 |year=1865b
 |title=Heat considered as a Mode of Motion
 |url=http://ia700304.us.archive.org/32/items/heatconsideredas00tyndrich/heatconsideredas00tyndrich.pdf
 |publisher=D. Appleton & Company
 }}
*{{chú thích tạp chí
 |last1=Wien |first1=W.
 |author1-link=Wilhelm Wien
 |year=1896
 |title=Über die Energievertheilung im Emissionsspectrum eines schwarzen Körpers
 |journal=Annalen der Physik und Chemie
 |volume=294
 |pages=662–669
 |doi= 10.1002/andp.18962940803
 |bibcode = 1896AnP...294..662W }}
*{{chú thích sách
 |last1=Wilson
 |first1=A. H.
 |year=1957
 |title=Thermodynamics and Statistical Mechanics
 |url=https://archive.org/details/thermodynamicsst0000wils
 |publisher=Cambridge University Press
 }}
{{cuối tham khảo}}

==Liên kết ngoài==
* [http://topex.ucsd.edu/rs/radiation.pdf Summary of Radiation]
* [http://www.vias.org/simulations/simusoft_blackbody.html Radiation of a Blackbody] – interactive simulation to play with Planck's law
* [http://scienceworld.wolfram.com/physics/PlanckLaw.html Scienceworld entry on Planck's Law]
* YAN Kun(2011). [http://www.nature.ac.cn/papers/paper-pdf/curveandequation-pdf.pdf Research on adaptive connection equation in discontinuous area of data curve] (Extended form of Einstein-Stern equation), DOI:10.3969/j.issn.1004-2903.2011.01.018.
{{sơ khai vật lý}}

{{DEFAULTSORT:Định luật Planck}}
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[[Thể loại:Max Planck]]