Answer to Question #113050 in General Chemistry for Nicole Dixon

Question

Since light is a form of Electromagnetic radiation/Electromagnetic Spectrum and Emission Spectra explain all aspects of its character, travel, and its characteristics based on work done in Quantum Mechanics:

Answer 1

In 1900 the German physicist Max Planck succeeded in calculating a blackbody spectrum that matched experimental results by proposing that the elementary oscillators at the surface of any object (the detailed structure of the oscillators was not relevant) could emit and absorb electromagnetic radiation only in discrete packets, with the energy of a packet being directly proportional to the frequency of the radiation, E = hf. The constant of proportionality, h, which Planck determined by by comparing his theoretical results with the existing experimental data, is now called Planck’s constant and has the approximate value 6.626×10^-34 J∙s.

Einstein supported his photon hypothesis with an analysis of the photoelectric effect, a process, discovered by Hertz in 1887, in which electrons are ejected from a metallic surface illuminated by light. Detailed measurements showed that the onset of the effect is determined solely by the frequency of the light and the makeup of the surface and is independent of the light intensity. This behaviour was puzzling in the context of classical electromagnetic waves, whose energies are proportional to intensity and independent of frequency. Einstein supposed that a minimum amount of energy is required to liberate an electron from a surface—only photons with energies greater than this minimum can induce electron emission. This requires a minimum light frequency, in agreement with experiment. Einstein’s prediction of the dependence of the kinetic energy of the ejected electrons on the light frequency, based on his photon model, was experimentally verified by the American physicist Robert Millikan in 1916.

In 1922 American Nobelist Arthur Compton treated the scattering of X-rays from electrons as a set of collisions between photons and electrons. Adapting the relation between momentum and energy for a classical electromagnetic wave to an individual photon, p = E/c = hf/c = h/λ, Compton used the conservation laws of momentum and energy to derive an expression for the wavelength shift of scattered X-rays as a function of their scattering angle. His formula matched his experimental findings, and the Compton effect, as it became known, was considered further convincing evidence for the existence of particles of electromagnetic radiation.

The energy of a photon of visible light is very small, being on the order of 4×10^-14 J. A more convenient energy unit in this regime is the electron volt (eV). One electron volt equals the energy gained by an electron when its electric potential is changed by one volt: 1 eV = 1.6 × 10^-19 J. The spectrum of visible light includes photons with energies ranging from about 1.8 eV (red light) to about 3.1 eV (violet light). Human vision cannot detect individual photons, although, at the peak of its spectral response (about 510 nm, in the green), the dark-adapted eye comes close. Under normal daylight conditions, the discrete nature of the light entering the human eye is completely obscured by the very large number of photons involved. For example, a standard 100-watt light bulb emits on the order of 1020 photons per second; at a distance of 10 metres from the bulb, perhaps 1011 photons per second will enter a normally adjusted pupil of a diameter of 2 mm.

Photons of visible light are energetic enough to initiate some critically important chemical reactions, most notably photosynthesis through absorption by chlorophyll molecules. Photovoltaic systems are engineered to convert light energy to electric energy through the absorption of visible photons by semiconductor materials. More-energetic ultraviolet photons (4 to 10 eV) can initiate photochemical reactions such as molecular dissociation and atomic and molecular ionization. Modern methods for detecting light are based on the response of materials to individual photons. Photoemissive detectors, such as photomultiplier tubes, collect electrons emitted by the photoelectric effect; in photoconductive detectors the absorption of a photon causes a change in the conductivity of a semiconductor material.

A number of subtle influences of gravity on light, predicted by Einstein’s general theory of relativity, are most easily understood in the context of a photon model of light and are presented here. (However, note that general relativity is not itself a theory of quantum physics.)

Through the famous relativity equation E = mc², a photon of frequency f and energy E = hf can be considered to have an effective mass of m = hf/c². Note that this effective mass is distinct from the “rest mass” of a photon, which is zero. General relativity predicts that the path of light is deflected in the gravitational field of a massive object; this can be somewhat simplistically understood as resulting from a gravitational attraction proportional to the effective mass of the photons. In addition, when light travels toward a massive object, its energy increases, and its frequency thus increases (gravitational blueshift). Gravitational redshift describes the converse situation where light traveling away from a massive object loses energy and its frequency decreases.

Quantum mechanics

The first two decades of the 20th century left the status of the nature of light confused. That light is a wave phenomenon was indisputable: there were countless examples of interference effects—the signature of waves—and a well-developed electromagnetic wave theory. However, there was also undeniable evidence that light consists of a collection of particles with well-defined energies and momenta. This paradoxical wave-particle duality was soon seen to be shared by all elements of the material world.

In 1923 the French physicist Louis de Broglie suggested that wave-particle duality is a feature common to light and all matter.

Wave-particle duality

The same interference pattern demonstrated in Young’s double-slit experiment is produced when a beam of matter, such as electrons, impinges on a double-slit apparatus. Concentrating on light, the interference pattern clearly demonstrates its wave properties. But what of its particle properties? Can an individual photon be followed through the two-slit apparatus, and if so, what is the origin of the resulting interference pattern? The superposition of two waves, one passing through each slit, produces the pattern in Young’s apparatus. Yet, if light is considered a collection of particle-like photons, each can pass only through one slit or the other. Soon after Einstein’s photon hypothesis in 1905, it was suggested that the two-slit interference pattern might be caused by the interaction of photons that passed through different slits. This interpretation was ruled out in 1909 when the English physicist Geoffrey Taylor reported a diffraction pattern in the shadow of a needle recorded on a photographic plate exposed to a very weak light source, weak enough that only one photon could be present in the apparatus at any one time. Photons were not interfering with one another; each photon was contributing to the diffraction pattern on its own.

In modern versions of this two-slit interference experiment, the photographic plate is replaced with a detector that is capable of recording the arrival of individual photons. Each photon arrives whole and intact at one point on the detector. It is impossible to predict the arrival position of any one photon, but the cumulative effect of many independent photon impacts on the detector results in the gradual buildup of an interference pattern. The magnitude of the classical interference pattern at any one point is therefore a measure of the probability of any one photon’s arriving at that point. The interpretation of this seemingly paradoxical behaviour (shared by light and matter), which is in fact predicted by the laws of quantum mechanics, has been debated by the scientific community since its discovery more than 100 years ago.