The Quantum Explanation of Spectral Lines

The explanation for exact spectral lines for each substance was provided by the quantum theory. In his 1913 model of the hydrogen atom Niels Bohr showed that the observed series of lines could be explained by assuming that electrons are restricted to atomic orbits in which their orbital angular momentum is an integral multiple of the quantity  h/2π, where h is Planck's constant. The integer multiple (e.g., 1, 2, 3 …) of h/2π is usually called the quantum number and represented by the symbol n.

When an electron changes from an orbit of higher energy (higher angular momentum) to one of lower energy, a photon of light energy is emitted whose frequency ν is related to the energy difference ΔE by the equation ν=ΔE/h.For hydrogen, the frequencies of the spectral lines are given by ν=cR (1/n_f²−1/n_i²) where c is the speed of light, Ris the Rydberg constant, and n_f and n_i are the final and initial quantum numbers of the electron orbits (n_i is always greater than n_f). The series of spectral lines for which n_f=1 is known as the Lyman series; that for n_f=2 is the Balmer series; that for n_f=3 is the Paschen series; that for n_f=4 is the Brackett series; and that for n_f=5 is the Pfund series. The Bohr theory was not as successful in explaining the spectra of other substances, but later developments of the quantum theory showed that all aspects of atomic and molecular spectra can be explained quantitatively in terms of energy transitions between different allowed quantum states.

Spectrum

Spectrum, arrangement or display of light or other form of radiation separated according to wavelength, frequency, energy, or some other property. Beams of charged particles can be separated into a spectrum according to mass in a mass spectrometer (see mass spectrograph). Physicists often find it useful to separate a beam of particles into a spectrum according to their energy.

Continuous and Line Spectra

Dispersion, the separation of visible light into a spectrum, may be accomplished by means of a prism or a diffraction grating. Each different wavelength or frequency of visible light corresponds to a different color, so that the spectrum appears as a band of colors ranging from violet at the short-wavelength (high-frequency) end of the spectrum through indigo, blue, green, yellow, and orange, to red at the long-wavelength (low-frequency) end of the spectrum. In addition to visible light, other types of electromagnetic radiation may be spread into a spectrum according to frequency or wavelength.

The spectrum formed from white light contains all colors, or frequencies, and is known as a continuous spectrum. Continuous spectra are produced by all incandescent solids and liquids and by gases under high pressure. A gas under low pressure does not produce a continuous spectrum but instead produces a line spectrum, i.e., one composed of individual lines at specific frequencies characteristic of the gas, rather than a continuous band of all frequencies. If the gas is made incandescent by heat or an electric discharge, the resulting spectrum is a bright-line, or emission, spectrum, consisting of a series of bright lines against a dark background. A dark-line, or absorption, spectrum is the reverse of a bright-line spectrum; it is produced when white light containing all frequencies passes through a gas not hot enough to be incandescent. It consists of a series of dark lines superimposed on a continuous spectrum, each line corresponding to a frequency where a bright line would appear if the gas were incandescent. The Fraunhofer lines appearing in the spectrum of the sun are an example of a dark-line spectrum; they are caused by the absorption of certain frequencies of light by the cooler, outer layers of the solar atmosphere. Line spectra of either type are useful in chemical analysis, since they reveal the presence of particular elements. The instrument used for studying line spectra is the spectroscope.

learn more: The Quantum Explanation of Spectral Lines

Conservation Laws

Conservation laws, in physics, basic laws that together determine which processes can or cannot occur in nature; each law maintains that the total value of the quantity governed by that law, e.g., mass or energy, remains unchanged during physical processes. Conservation laws have the broadest possible application of all laws in physics and are thus considered by many scientists to be the most fundamental laws in nature.

Conservation of Classical Processes

Most conservation laws are exact, or absolute, i.e., they apply to all possible processes; a few conservation laws are only partial, holding for some types of processes but not for others. By the beginning of the 20th cent. physics had established conservation laws governing the following quantities: energy, mass (or matter), linear momentum, angular momentum, and electric charge. When the theory of relativity showed (1905) that mass was a form of energy, the two laws governing these quantities were combined into a single law conserving the total of mass and energy.

Conservation of Elementary Particle Properties

With the rapid development of the physics of elementary particles during the 1950s, new conservation laws were discovered that have meaning only on this subatomic level. Laws relating to the creation or annihilation of particles belonging to the baryon and lepton classes of particles have been put forward. According to these conservation laws, particles of a given group cannot be created or destroyed except in pairs, where one of the pair is an ordinary particle and the other is an antiparticle belonging to the same group. Recent work has raised the possibility that the proton, which is a type of baryon, may in fact be unstable and decay into lighter products; the postulated methods of decay would violate the conservation of baryon number. To date, however, no such decay has been observed, and it has been determined that the proton has a lifetime of at least 10³¹ years. Two partial conservation laws, governing the quantities known as strangeness and isotopic spin, have been discovered for elementary particles. Strangeness is conserved during the so-called strong interactions and the electromagnetic interactions, but not during the weak interactions associated with particle decay; isotopic spin is conserved only during the strong interactions.

Conservation of Natural Symmetries

One very important discovery has been the link between conservation laws and basic symmetries in nature. For example, empty space possesses the symmetries that it is the same at every location (homogeneity) and in every direction (isotropy); these symmetries in turn lead to the invariance principles that the laws of physics should be the same regardless of changes of position or of orientation in space. The first invariance principle implies the law of conservation of linear momentum, while the second implies conservation of angular momentum. The symmetry known as the homogeneity of time leads to the invariance principle that the laws of physics remain the same at all times, which in turn implies the law of conservation of energy. The symmetries and invariance principles underlying the other conservation laws are more complex, and some are not yet understood.

Three special conservation laws have been defined with respect to symmetries and invariance principles associated with inversion or reversal of space, time, and charge. Space inversion yields a mirror-image world where the "handedness" of particles and processes is reversed; the conserved quantity corresponding to this symmetry is called space parity, or simply parity, P. Similarly, the symmetries leading to invariance with respect to time reversal and charge conjugation (changing particles into their antiparticles) result in conservation of time parity, T, and charge parity, C. Although these three conservation laws do not hold individually for all possible processes, the combination of all three is thought to be an absolute conservation law, known as the CPT theorem, according to which if a given process occurs, then a corresponding process must also be possible in which particles are replaced by their antiparticles, the handedness of each particle is reversed, and the process proceeds in the opposite direction in time. Thus, conservation laws provide one of the keys to our understanding of the universe and its material basis.