Date of Award
2024
Document Type
Thesis
Degree Name
Bachelors
Department
Natural Sciences
First Advisor
Sendova, Mariana
Area of Concentration
Physics
Abstract
The study proposes generalizations of 18 mathematical forms of Planck’s thermal radiation law. Sixteen transcendental equations are derived and solved for calculating the positions of three characteristic points: two inflection points and a maximum. Displacement laws for each of the characteristic points (total of 52 points), in the spirit of Wien’s displacement law, are proposed. The study analyzes eight unitless probability density functions (PDFs) via proposed inflection point parameters, compared to the conventional standard deviation statistical parameter. Additionally, the proposed comparative study is utilized as a framework for linking Photobiological processes and the Planck’s thermal radiation law. It is proposed that 91% of the bio-photons are bound between the two inflection points of the per-wavelength photon radiance PDF, expressed as a function of the photon energy. Finally, the study suggests extensions of the generalization of Planck’s thermal radiation law to the realm of solid-state phonons.
Recommended Citation
Moncada-Almendarez, Isaac, "Generalization of Planck’s Law and Analysis of Inflection Points and Maxima" (2024). Theses & ETDs. 6574.
https://digitalcommons.ncf.edu/theses_etds/6574