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Oxford University Press eBooks

The emergence of quantum theory

Peter Joshua Atkins, Julio de Paula, David Young Smith

Published Dec 15, 2016• 0 citations
Publisher

Abstract

This chapter looks at the experimental evidence towards the end of the nineteenth century that showed that classical mechanics failed when it was applied to very small particles and when the transfers of energy were very small. It discusses classical mechanics and shows how it predicts a precise trajectory for particles, with specified locations and moments at each instant. It also describes experiments which have showed that energy was transferred only in discrete amounts and showed that electromagnetic radiation behaves like a stream of particles. The chapter analyzes how electrons, which had been supposed to be particles since their discovery in 1897, can behave like waves. It reviews the translational, rotational, and vibrational modes of motion that are excited to any energy simply by controlling the forces that are applied.

DOI
10.1093/hesc/9780198727873.003.0045

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This chapter looks at the experimental evidence towards the end of the nineteenth century that showed that classical mechanics failed when it was applied to very small particles and when the transfers of energy were very small. It discusses classical mechanics and shows how it predicts a precise trajectory for particles, with specified locations and moments at each instant. It also describes experiments which have showed that energy was transferred only in discrete amounts and showed that electromagnetic radiation behaves like a stream of particles. The chapter analyzes how electrons, which had been supposed to be particles since their discovery in 1897, can behave like waves. It reviews the translational, rotational, and vibrational modes of motion that are excited to any energy simply by controlling the forces that are applied.
This chapter traces the origins of quantum mechanics. The classical mechanics developed by Isaac Newton in the seventeenth century is an extraordinarily successful theory for describing the motion of everyday objects and planets. However, late in the nineteenth century, scientists started to make observations that could not be explained by classical mechanics. They were forced to revise their entire conception of the nature of matter and replace classical mechanics by a theory that became known as quantum mechanics. The chapter begins by looking at energy quantization, considering black-body radiation, heat capacity, and atomic and molecular spectra. It then discusses wave–particle duality, which is the recognition that the concepts of particle and wave blend together.
This chapter examines the historical development of quantum mechanics, focusing on key experiments and theories that challenged classical physics. It begins with blackbody radiation, highlighting the discrepancy between classical predictions and experimental observations, leading to Planck's quantization hypothesis, which posits that energy is emitted in discrete packets (quanta). The chapter covers the photoelectric effect and Compton scattering, demonstrating wave–particle duality and validating quantum theory. It also discusses atomic models, culminating in the Bohr model and the energy-level diagram of the hydrogen atom, which explains atomic phenomena such as line spectra and discrete energy transitions. The chapter concludes by introducing the quantum model, which supersedes the Bohr model by incorporating wave–particle duality and the uncertainty principle, highlighting the necessity of quantum mechanics for accurate atomic-scale descriptions.
Science has developed through a variety of investigations more or less over the time scale of human existence. On this scale, quantum mechanics is an extremely young field, existing essentially for only just over a century. Even our understanding of classical mechanics has existed for a comparatively long period—roughly having been formalized with Newton's equations published in his Principia Mathematica , in April 1686 (1687). Up until the very end of the nineteenth century, mechanics in the form of Newton's laws were comfortable, being understood and accepted by all who dealt with the motion of reasonable bodies. With the turn of the new century, however, mechanics would be shaken to its roots. The change began already on December 14, 1900, when Planck (1900) presented his new theory of black-body radiation to the German Physical Society, and this change would affect mechanics in physically small structures (and lead to quantum mechanics). Mechanics of large bodies would similarly be changed in 1905 with the arrival of Albert Einstein's (1905a) relativity theory. In this book, we will deal with only the first of these two great breakthroughs.
Quantum mechanics is the study of matter and radiation at an atomic level. It is a mathematical tool for predicting the behaviours of microscopic particles. This chapter discusses the historical background of quantum theory. Planck's idea of discrete energy of a harmonic oscillator implies that the frequencies for the absorbed and emitted radiation should be discrete. According to classical physics, a system can absorb or emit any amount of energy. In 1902 Phillip Edward Anton Von Lenard, an assistant of Hertz, studied photoelectric effect. His setup consisted of a photocell connected to a circuit with a power supply, voltmeter and micro-ammeter. The Franck–Hertz experiment gave an evidence of discrete energy levels of atoms. The particle nature of radiation is established by the Compton effect. Lasers, semiconductors and superconductors are just few among the various applications of the most radical predictions of quantum mechanics.
Introduction While it might appear that the nineteenth-century physics presented in this chapter has no place in a topic as quantum mechanically oriented as atomic physics, this is simply not the case. The purpose of this first chapter is to try to convince the readers that the material learned in their early years of studying physics is not disjoint from modern topics, but in fact can provide a foundation for their further understanding. Other examples will occur later. The reader may be a bit surprised to see that the results of the classical description turn out to be so close to the quantum mechanical results. Where there are significant disagreements between classical and quantum descriptions, it is necessary to explain why these occur. The correspondence principle requires that in the limit of large quantum numbers the complete quantum mechanical description must agree with the classical one. It is always better to need fewer of these explanations and to be able to treat physics as a coherent whole instead of a collection of topics. The consequences of classical physics are intuitively familiar, and this is often most helpful in gaining deeper understanding. In fact, the approach taken in very many of the chapters in this book is to start with a purely classical description of a topic, and then transport it directly into the Schrödinger equation. Radiation from an accelerated charge, as treated here in the harmonic case, provides an ideal setting for such pedagogy. Even though classical mechanics is used in place of quantum mechanics, for the case of harmonic motion, the results are quite compatible. The early history of atomic physics contains many topics that are well worth reading about, especially the experimental facilities. For example, there were no electric motors, wire was not readily available, and making even a crude vacuum was an experimental tour de force. Very many textbooks have discussions of these topics, and so they will not be presented here. But the reader is warned that certain oft-repeated modern descriptions are simply wrong. Perhaps the most important notion to be gained from this chapter is that the classical description of a harmonically bound electron provides quite accurate results about the interaction between atoms and light. Of course, the utility of this description is limited because the classical harmonic oscillator has no internal structure, is infinitely deep, and has a continuous energy spectrum.