Creating A New Planck’s Formula of Spectral Density of Black-body Radiation by Means of AF(A) Diagram

This paper reports derivation of a new Planck’s formula of spectral density of black-body radiation, that was originated by modeling the interpolation formula of Planck’s law of obtaining the mean of energy of black-body cavity in 2^nd order of Bernoulli equation. The new Planck’s formula is created by means AF(A) diagram of solving arctangent differential equation after transformin the Bernoulli equation into the arctangent differential equation The New Planck’s formula not only contains the terms of the photon energy and the energy difference between two states of the motion of harmonic oscillator (), but also contains both terms of the minimum energy of harmonics oscillator () and the phase differences () as representing the intermodes-orthogonality, hence it can answer why the explanation of black-body radiation has been associated with the harmonic oscillators.

I. Introduction

The era of developing the modern scientific was originated by presence the Planck’s law of black-body radiation as representation of the light sources in a thermal equilibrium. Planck not only could complete the Rayleigh-Jeans and Wien’s laws, both of radiation laws previously that of each only appropriates to the experimental for the range of long wavelength and short wavelength respectively, but he also created a new constant h called as Planck’s constant that not known previously in classical physics [1]. Based on his constant, Planck postulated the discretitation of electromagnetic energy in packet of energy called as photon, where for every angular frequency (), the energy per photon is , which was justified later by Einstein through fotoelectric effect [2]. Planck’s law for black-body radiation also became the primary base of derivation Einstein coefficients of spontaneous and stimulated of emission rates for generating the light sources such as maser and laser [3].

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