Quantum theory

Abstract

In the early 1900's, Modern Physics started to be developed. Before Max Planck started his research in the blackbody ray, the related available results were waiting for a new concept of energy. The blackbody, that is a closed empty cavity impermeable for any exterior ray, at the temperature T, and containing a hole to allow the interior ray to exit from the cavity; emits a themal ray inside the cavity, in the electromagnetic radiations form with all possible wavelengths, once the equilibrium is reached between the cavity wall and the interior thermal ray. The blackbody spectral energy density u(ν,T) is an universal function of the frequency anf the temperature. The total energy density u(T) in the cavity is an universal function of the temperature whish is given by the Stefan law u(T) = a T⁴. The emissive power of the blackbody is given by P = σT⁴; where σ = ac/4. At this time the numerical values of c (speed of light), a, and σ were well defined: σ = 5.6 to 5.7 x 10^-5 CGS, c ≈ 3.0 x 10⁸ m.sec^-1, and a = 7.57 x 10^-15 CGS.The established experimental results had given the profiles of the curves u(ν,T) with respect to the frequency at a given temperature. The curves are in "bell" shape in which the maximum abscissa ν_m is linked to the temperature by the relationship ν_m/T (or λ_mT = constant), called the Wien displacement. Wien has given also the exacte form of the spectral energy density u(ν,T) in the form of u(ν,T) = T³ u(ν/T), which remains undefined. Rayleigh and Jeans used the statistical mechanics, and made the assumption that each electromagnetic radiation is anlogous to a linear oscillator and the mode of the cavity is the mode corresponding to the states of the set of the oscillators. The related mode corresponds to a standing vibrational polarized waves. According to the energy equipartition principle (E = kT), the two physicists Rayleigh and Jeans had given the expression of the spectral energy density u(ν,T) = (8π/c³) (R/Na) T ν²; where R is the ideal gas constant ≈ 8.314 joules.mole^-1oK^-1, and Na is the Avogadro number ≈ 6.02 x 10²³ mol^-1. Boltzmann used R/A ( A is the Avogadro number); that becomes k = R/A, wrote by Planck and becomes the Boltzmann constant. The established Rayleigh-Jeans formula was not correct and predicted an infinite energy for the short wavelengths, especially un the UV region. Ehrenfest had called this prediction the ultraviolet catastrophe. Max Planck had known these former results related to the blackbody. He made an ad hoc supposition that he had made a postulate: "The energy exchange between material and thermal ray is an integral multiple of quanta". Each quantum hold an energy equal to hν, where h is a constant and ν the corresponding wave frequency. That was the first statement of the "quantization of energy".