This chapter addresses the question of whether light consists of waves or particles. This issue was resolved in the nineteenth century when it was shown that light could undergo interference and diffraction. The chapter reviews well-known properties and key features of wave motions that emphasize that a point illuminated by two sources of light can nevertheless be in darkness. It also looks at the measurements of diffraction experiments that allowed the wavelengths of different forms of light to be determined. The chapter explains how and why atoms come together to form molecules and illustrates the structure of the Periodic Table. It discusses electrons which are emitted from metal when the energy of the photon exceeds the work function, which implies that a single quantum of energy must be transferred to a single electron.
This chapter addresses the question of whether light consists of waves or particles. This issue was resolved in the nineteenth century when it was shown that light could undergo interference and diffraction. The chapter reviews well-known properties and key features of wave motions that emphasize that a point illuminated by two sources of light can nevertheless be in darkness. It also looks at the measurements of diffraction experiments that allowed the wavelengths of different forms of light to be determined. The chapter explains how and why atoms come together to form molecules and illustrates the structure of the Periodic Table. It discusses electrons which are emitted from metal when the energy of the photon exceeds the work function, which implies that a single quantum of energy must be transferred to a single electron.
Abstract In this chapter, we explore the nature of light and atoms, focusing on their dual nature as both particles and waves. We examine why atoms have discrete energy levels and how only certain frequencies of light can excite electrons within these atoms. Through this exploration, we will understand the relationship between light’s frequency, wavelength, and photon energy. We also explore key concepts such as wave interference and the historical experiments that shaped our understanding of quantum mechanics. Most importantly, this chapter emphasizes the scientific method, encouraging continual questioning of ideas, understanding, theories, and results to uncover the fundamental nature of the universe.
Since the beginning of the 20th century, physicists have known that light must be considered as both a wave and a particle. Some properties of light – such as diffraction – can only be explained by treating it as waves, while others – like the photoelectric effect – can only be explained by treating it as particles. In the 1920s Louis de Broglie suggested that this wave–particle duality, which lies at the heart of the counterintuitive laws of quantum mechanics, could be extended to massive particles. In other words, electrons, atoms and molecules should diffract and interfere just like light does.
At the atomic scale, the distinction between particles and waves breaks down. The realization, early in the twentieth century, that light consists of discrete packages, or “photons,” prompted the converse suggestion that particles could behave like waves. Confirmation of this idea came in 1927, from an experiment involving the scattering of electrons from a crystal. Today, “wave-particle duality” is central to quantum mechanics, and the wave properties of subatomic particles are widely used in microscopy and crystallography. Electron diffraction techniques are widely used to characterize atomic arrangements on solid surfaces and inside thin films, and to investigate the structures of molecules in gases. The dual nature of waves and particles is part of the “spookiness” of quantum mechanics, which cannot be explained in any classical way. It used to be that one could only imagine an experiment that would simultaneously demonstrate the particle and wave nature of electrons.
This chapter begins with a brief outline of some of the key motivations for considering a quantum theory: the early attempts to determine the spectral distribution of energy density of black bodies; stability of atoms and molecules; specific heats of solids; interference and diffraction of light beams; polarization of photons. The experimental foundations of wave mechanics are then presented in detail, but in a logical order quite different from its historical development: photo-emission of electrons by metallic surfaces, X- and γ-ray scattering from gases, liquids and solids, interference experiments, atomic spectra and the Bohr hypotheses, the experiment of Franck and Hertz, the Bragg experiment, diffraction of electrons by a crystal of nickel (Davisson and Germer), and measurements of position and velocity of an electron. The need for a quantum theory In the second half of the nineteenth century it seemed that the laws of classical mechanics, developed by the genius of Newton, Lagrange, Hamilton, Jacobi and Poincaré, the Maxwell theory of electromagnetic phenomena and the laws of classical statistical mechanics could account for all known physical phenomena. Still, it became gradually clear, after several decades of experimental and theoretical work, that one has to formulate a new kind of mechanics, which reduces to classical mechanics in a suitable limit, and makes it possible to obtain a consistent description of phenomena that cannot be understood within the classical framework. It is now appropriate to present a brief outline of this new class of phenomena, the systematic investigation of which is the object of the following sections and of chapters 4 and 14.
The long history of the dispute among physicists as to whether matter is composed of particles or waves is reviewed. A turning point came at the dawn of the 20th century in the form of the de Broglie momentum-wavelength and Bohr/Planck energy frequency relations. It was on this basis that Schrödinger developed a quantum mechanical differential equation whose solution came to be known as a wave function. The Born Interpretation of these functions holds that their absolute square constitutes a probability distribution which has been used successfully to make predictions of the properties of the system under discussion. It is pointed out that the phenomenon of light refraction played a key role in the development of both Newton’s corpuscular theory of light and the competing theory of Huygens which looks upon light as consisting exclusively of waves. It is shown that Newton’s failure to predict the decrease in the speed of light as it passes from air into water was not because of his belief in the particle composition of light, but rather because he not did anticipate that the mass of a photon changes upon entering a medium of higher index of refraction n. By assuming that the energy E of light is equal pc/n, where p is the momentum of the photons and c is the speed of light in free space, it is shown that the experimental dependence of the speed the light on its wavelength as it passes through a transparent medium is derived successfully through the use of Hamilton’s Canonical Equations and Newton’s Second Law of Kinetics. It is suggested that the relationship between particles and waves can be understood by noting that the localized properties of matter exhibit themselves in experiments such as the photoelectric effect where attention can be concentrated on the behavior of a single particle. The corresponding wave properties occur when large numbers of particles are observed under exactly similar circumstances, as for example in electron diffraction. ...........
This chapter introduces fundamental concepts of modern physics that emerged from groundbreaking experiments and theories in the early 20th century. It begins by exploring the photoelectric effect, which demonstrates the particle nature of light (photons) and provides a basis for mathematical analysis of this phenomenon. The chapter then discusses Bragg diffraction and the concept of the wave function, illustrating the wave nature of particles such as electrons, protons, and neutrons, and introducing the idea of wave-particle duality. The probability distribution for an electron, whether trapped in a well or traveling freely, is also examined. Rutherford scattering is presented as a pivotal experiment that revealed the existence of the positively charged atomic nucleus. The chapter further explores atomic spectra, explaining how the discrete wavelengths of emitted light indicate that atomic electrons have restricted, quantized energy levels. The Bohr model of the atom is described and mathematically analyzed to predict the spectrum of hydrogen. Finally, the chapter covers the Balmer-Rydberg formula for mathematically analyzing the spectrum of hydrogen. The content is organized into sections covering the photoelectric effect, Bragg diffraction and the wave function, Rutherford scattering, atomic spectra, and a summary of the key concepts. This chapter provides an introduction to the revolutionary ideas of modern physics, including the dual nature of light and matter and the quantized nature of the atom. The chapter includes numerous worked examples and concludes with problems for the student to apply their knowledge.