Independent researcher in Prague, Czechia
* Corresponding author

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There were derived many forms of the Planck distribution function (PDF) since its discovery by Planck in 1900 and formulae for the positions of Wien´s peaks in those distributions. There are three features of the Solar photons – their refrangibility, their heat effect, and their chemical effect. The first feature – their refrangibility – can be modelled using the linear-wavelength dispersion rule for spectrometers with diffraction gratings and using the frequency-square rule for spectrometers with prisms. However, there are no accepted forms of the PDF to model heat effect of the Solar photons on atoms and molecules, and to model the effect of the PDF on chemical reactions where the Solar photons play very significant role. We have summarized the known forms of the PDF and positions of Wien´s peaks in order to search some hidden properties in those mathematical structures. It will be shown that these very well-known formulae to all scholars might still keep some hidden surprising properties.

References

  1. Wien W. Eine neue Beziehung der Strahlung schwarzer Körper zum zweiten Hauptsatz der Wärmetheorie. Sitzungsberichte der Königlich Preussischen Akademie der Wissenschaften zu Berlin. 1893; S. 55. German.
     Google Scholar
  2. Wien W. Űber die Energievertheilung im Emissionspectrum eines schwarzen Körpers. Annalen der Physik und Chemie. 1896; 294(8): 662-669. German.
     Google Scholar
  3. Planck M. Űber eine Verbesserung der Wien´schen Spectralgleichung. Verhandlungen der Deutschen Physikalischen Gesselschaft. 1900; 2: 202-204. German.
     Google Scholar
  4. Einstein A. Űber einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt. Annalen der Physik. 1905; 17: 164-181. German.
     Google Scholar
  5. Nernst W. (Editor). Die Theorie der Strahlung und der Quanten. Verhandlungen auf einer von E. Solvay einberufenen Zusammenkunft (30. Oktober bis 3. November 1911). Knapp Verlag, Halle a.S., 1914. German.
     Google Scholar
  6. Kangro H. Vorgeschichte des Plankschen Strahlungsgesetzes. Messungen und Theorien der Spektralen Energieverteilung bis zur Begründung der Quantenhypothese. Franz Steiner Verlag, Wiesbaden, 1970. German.
     Google Scholar
  7. Kuhn TS. Black-body theory and the quantum discontinuity, 1894-1912. The University Chicago Press, 1978.
     Google Scholar
  8. Gershun AA. On the spectral density of radiation. Uspekhi Fizicheskich Nauk. 1952; (3): 388-395. Russian.
     Google Scholar
  9. Foitzik L. Űber die Darstellung der spektkralen Energieverteilung von Strahlungsquellen. Experimentelle Technik der Physik. 1953; 1953(4/5): 209-213. German.
     Google Scholar
  10. Bracewell RN. The maximum of the Planck energy spectrum. Nature (London). 1954; 4429: 563-564.
     Google Scholar
  11. Gurevich MM. On the spectral distribution of radiant energy. Uspekhi Fizicheskikh Nauk. 1955; 56(3): 417-424.
     Google Scholar
  12. Sapozhnikov RA. Spectral distribution of radiant energy. Soviet Physics Uspekhi. 1960; 3(1): 172-174.
     Google Scholar
  13. Chiu WC. On the interpretation of the energy spectrum. American Journal of Physics. 1967; 35(7): 642-648.
     Google Scholar
  14. Soffer BH, Lynch DK. Some paradoxes, errors, and resolutions concerning the spectral optimization of human vision. American Journal of Physics, 1999; 67(11): 946-953.
     Google Scholar
  15. Overduin JM. Eyesight and the Solar Wien peak. American Journal of Physics, 2003; 71(3): 216-219.
     Google Scholar
  16. Heald MA. Where is the „Wien peak“? American Journal of Physics, 2003; 71(12): 1322-1323.
     Google Scholar
  17. Kramm G, Mölders N. Planck´s blackbody radiation law: presentation in different domains and determination of the rrelated dimensional constants. Arxiv: 0901.1863v2.
     Google Scholar
  18. Zhang ZM, Wang XJ. Unified Wien´s displacement law in terms of logarithmic frequency or wavelength scale. Journal of Thermophysics and Heat Transfer. 2010; 24(1): 222-224.
     Google Scholar
  19. Stewart SM. Wien peaks and the Lambert W function. Revista Brasileira de Ensimo de Física. 2011; 33(3): 3308.
     Google Scholar
  20. Stewart SM. Spectral peaks and Wien´s displacement law. Journal of Thermophysics ad Heat Transfer. 2012; 26(4): 689-691.
     Google Scholar
  21. Marr JM, Wilkin FP. A better presentation of Planck´s radiation law. Arxiv: 1109.3822v3.
     Google Scholar
  22. Deldago-Bonal A. Entropy of radiation: the unseen side of light. Scientific Reports. 2017; 7: 1642.
     Google Scholar
  23. Hagen N. Spectra, images, simple functions, and density functions. 2021 11th Workshop on hyperspectral imaging and signal processing: evolution in remote sensing (WHISPERS), Amsterdam, Netherlands, 2021, pp. 1-5.
     Google Scholar
  24. Kostić L, Mančev I. Lambert W function ad different forms of Wien´s displacement law. Romanian Reports in Physics. 2021; 73: 906.
     Google Scholar
  25. Calculation of blackbody radiance. Arxiv: 2108.03119. Last accessed Janaury 24, 2023.
     Google Scholar
  26. Gnanarajan S. Application of Lambert W function to Planck spectral radiance frequencies. Journal of Applied Mathematics and Physics, 2021; 9: 2500-2510.
     Google Scholar
  27. Marcus Marci J. Thaumantias, Liber de arcu coelesti, deque colorum apparentium, natura, ortu et causis. Prague 1648; reproduced 1968. Latin.
     Google Scholar
  28. Marek J. Marcus Marci´s results in the optics of radiation. In Joannes Marcus Marci – A seventeenth-century Bohemian polymath, Svobodny P. (Ed.), Charles University Press, Prague; 1998. ISBN 80-7184-475-6.
     Google Scholar
  29. Garber MD. Chymical wonders of light: J. Marcus Marci´s seventeenth-century Bohemian optics. Early Science and Medicine, 2005; 10(4): 486-518.
     Google Scholar
  30. Newton I. Optics or a treatise of the reflections, refractions, inflections, & colours of light. Dover Publications, 2014.
     Google Scholar
  31. Westfall RS. The development of Newton´s theory of color. Isis. 1962; 53(3): 339-358.
     Google Scholar
  32. Rochon AM. (1783). Sur la degré de chaleur des rayons colorés. English trans. An essay on the degree of warmth of coloured rays. Philosophical Magazine. 45: 410-414.
     Google Scholar
  33. Wünsch CE. Versuche über die vermeinte Sonderung des Lichtes der Sonnenstrahlen von der Wärme derselben. Magazin der Gesselschaft Naturforschende Freunde zu Berlin. 1807; 185-207. German
     Google Scholar
  34. Seebeck TJ. Ueber die ungleiche Erregung der Wärme im prismatischen Sonnebilde. Abhandlungen der königlichen Akademie der Wissenschaften in Berlin aus den Jahren 1818-1819. Berlin, 1820, pp. 305-350. German.
     Google Scholar
  35. Seebeck TJ. On the unequal evolution of heat in the prismatic spectrum. Philosophical Magazine. 1825; 66: 330-343, 445-455.
     Google Scholar
  36. Cornell ES. The radiant heat spectrum from Herschel to Melloni I. The work of Herschel and his contemporaries. Annals of Science. 1938; 3: 119-137.
     Google Scholar
  37. Cornell ES. The radiant heat spectrum from Herschel to Melloni II. The work of Melloni and his contemporaries. Annals of Science. 1938; 3: 402-413.
     Google Scholar
  38. Barr ES. Historical survey of the early development on the infrared spectral region. American Journal of Physics. 1960; 28: 42-54.
     Google Scholar
  39. Barr ES. The infrared pioneers – I. Sir William Herschel. Infrared Physics. 1961; 1: 1-10.
     Google Scholar
  40. Hentschel K. Mapping the spectrum. Techniques of visual representation in research and teaching. Oxford University Press, Oxford, 2009, Ch. 2, pp. 21-72.
     Google Scholar
  41. Herschel W. Investigations of the powers of the prismatic colours to heat and illuminate objects; with remarks that prove the different refrangibility of radiant heat. Philosophical Transactions of the Royal Society, London. 1800; pp. 255-283, 284-292, 293-326, 437-538.
     Google Scholar
  42. Lowell DJ. Herschel´s dilemma in the interpretation of thermal radiation. Isis. 1968; 59(1): 46-60.
     Google Scholar
  43. Hilbert M. Herschel´s investigation of the Nature of radiant heat: the limitations of experiment. Annals of Science. 199; 56: 357-378.
     Google Scholar
  44. Minkina W. How infrared radiation was discovered – range of this discovery and detailed, unknown information. Applied Sciences. 2021; 11: 9824.
     Google Scholar
  45. Kangro H. Vorgeschichte des Plankschen Strahlungsgesetzes. Messungen und Theorien der Spektralen Energieverteilung bis zur Begründung der Quantenhypothese. Franz Steiner Verlag, Wiesbaden, 1970. German. pp. 23-26.
     Google Scholar
  46. Ghosh G. Handbook of Refractive Index and Dispersion of Water for Scientists and Engineers: Optic and Pressure-Optic Coefficients of Water. Independent Publisher; 2021.
     Google Scholar
  47. Wikipedia.org Refractive index. Available from https://en.wikipedia.org/wiki/Refractive_index [updated 2022 December 22; cited 2023 January 22].
     Google Scholar
  48. Chang SL, Rhee KT. Blackbody radiation functions. International Communications in Heat and Mass Transfer. 1984; 11(5): 451-455.
     Google Scholar
  49. Jain PK. IR, visible, and UV components in the spectral distribution of blackbody radiation. Physics Education, 1996; 31:149-155.
     Google Scholar
  50. Lawson D. A closer look at Planck´s blackbody equation. Physics Education. 1997; 35(5): 321-326.
     Google Scholar
  51. Lawson DL. The blackbody fraction, infinite series and spreadsheets. International Journal of Engineering Education. 2004; 20(6): 984-900.
     Google Scholar
  52. Ritter JW. Am 22sten Februar (Discovery of UV light). Annalen der Physik. 1801; 7, 527. German.
     Google Scholar
  53. Link HF. Ueber die chemischen Eigenschaften des Licht: Versuch einer Beantwortung der von Kaiserlichen Akademie der Wissenschaften zu Petersburg aufgeworfenen Frage. St. Petersburg: Kaiserliche Akademie der Wissenschaften.1808. German.
     Google Scholar
  54. Hentschel K. Unsichtbares Licht? Dunkle Wärme? Chemische Strahlen? Eine wissenschaftshistorische und -theoretische Analyse von Argumenten für das Klassifizieren von Strahlungsorten 1650-1925 mit Schwerpunkt auf den Jahren 1770-1900. GNT-Verlag GmbH, 2007. ISBN-10: 3928186841. German.
     Google Scholar
  55. Frercks J, Weber H, Wiesenfeldt G. Reception and Discovery: the nature of Johann Willhelm Ritter´s invisible rays. Studies in History and Philosophy of Science. 2009; 40: 143-156.
     Google Scholar
  56. Balzani V, Ceroni P, Juris A. Photochemistry and Photophysics: concepts, research, applications. Wiley-CH. 2014. ISBN-10: 9783527334797.
     Google Scholar
  57. Albini A. Photochemistry: past, present and future. Springer. 2016. ISBN-10: 3662507811
     Google Scholar
  58. Persico M, Granucci G. Photochemistry: A modern theoretical perspective (Theoretical chemistry and computational modelling). Springer. 2019. ISBN-10: 3030079066.
     Google Scholar


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