Quantum Theory

Abstract

The quantum theory arose in the first instance out of attempts to explain the distribution of energy in the continuous spectrum of an incandescent body. As a piece of metal is heated to incandescence it first becomes red at about 850 K. Later, as the temperature rises further, it becomes yellow and then white at about 3000 K, when all the visible spectrum is being radiated. Experimental investigation of the energy distribution for various temperatures, yields curves of the form shown in Fig. 6.1. It is at once apparent that, as the temperature rises, not only does the energy increase, but the wavelength of maximum energy λ_max moves to the region of shorter wavelength. Analysis of the curves shows that λ_maxT =constant. This formula can be derived using the thermodynamical reasoning of classical physics and is known as Wien’s displacement law. Wien also showed that the form of the curve could be represented empirically by a formula E _λ =C₁ λ⁻⁵ exp (— C₂/λT), where C₁, C₂ are constants and E _λ is the energy radiated at wavelength λ. This formula is in very close agreement with experiment for small values of T in the visible spectrum corresponding to temperatures up to 2000 K, but diverges for larger values of λT. It also gave the displacement law λ_maxT =constant. (See Problem 6.14.)