Therefore, Planck’s law reduces to Rayleigh – Jeans law for longer Therefore Planck’s law reduces to Wien’s displacement for smaller wavelengths. Hence, ‘1’ is neglected in the denominator When λ is small, γ is very large, hence is large when compared to 1. It can also be expressed in terms of frequencies by substitutingĢ.1 DEDUCTION OF WIEN’S DISPLACEMENT LAW: This law explained significantly the entire blackbody spectrum. This equation represents Planck’s radiation law in terms of wavelength. The energy density of radiation between wavelengths λ and λ+dλ is given byĮ λdλ = (Number of oscillators per unit volume in the interval λ and λ+dλ) x (Average energy per oscillator) Number of oscillators per unit volume in the wavelength range λ and λ+dλ is given by We know from Planck’s quantum theory, ɛ can be a quanta of integral values of hγ and so the possible values of ɛ are 0, 2hγ, and 3hγ etc. Let N be the total number of Planck’s oscillators and N 1, N 2, N 3 etc be the number of oscillators with energies ɛ 0, ɛ 1, ɛ 2. Number of atomic oscillators in ground state = N 0įrom Maxwell’s distribution law, the number of oscillators having energy ɛ n in excess of ground state energy ( ɛ 0 ) is given by Where E is the total energy and N is the number of oscillators. The energy density of heat radiation emitted from an enclosure at temperature T in the wavelength range from λ to λ + λd is given byĢ DERIVATION OF PLANCK’S LAW OF RADIATIONĪssume that a black body consists of energy by a large number of atomic oscillators. The emission of radiation corresponds to a decrease and absorption to an increase in the energy and amplitude of an oscillator. The oscillator can have only discrete energy E n given by If an oscillator is vibrating with a frequency γ, it can radiate in quantas of magnitude h γ. It can emit energy in the multiples of a small unit called Quantum (Photon). An oscillator cannot emit energy in a continuous manner. The frequency of radiation emitted by an oscillator is the same as the frequency of its vibration.Ĭ. They can vibrate with all possible frequencies.ī. A black body chamber is filled up not only with radiation, but also with simple harmonic oscillators or harmonic oscillators or resonators of molecular dimensions. He derived the radiation law by using the following assumptions.Ī. Planck suggested in deriving the formula, which agrees extremely well with experimental results. He suggested quantum theory of radiation. Planck suggested that the correct results could be obtained if the energy of oscillating electrons is taken as discrete rather than continuous.
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