Compton Effect

Compton Effect 

  

The elastic scattering of electromagnetic radiation by free electrons, accompanied by an increase in wavelength; it is observed during scattering of radiation of short wavelength—X rays and gamma rays. The corpuscular properties of radiation were fully revealed for the first time in the Compton effect. 

The Compton effect was discovered in 1922 by the American physicist A. Compton, who observed that X rays scattered in paraffin have a longer wavelength than the incident rays. Such a shift in wavelength could not be explained by classical theory. In fact, according to classical electrodynamics, under the influence of the periodic electric field of an electromagnetic (light) wave, an electron should oscillate with a frequency equal to that of the wave and consequently should radiate secondary (scattered) waves of the same frequency. Thus, in “classical” scattering (the theory of which was provided by the British physicist J. J. Thomson and is therefore called Thomson scattering) the wavelength of the light does not change. 

An elementary theory of the Compton effect based on quantum concepts was given by Compton and independently by P. Debye. According to quantum theory a light wave is a stream of light quanta, or photons. Each photon has a definite energy ع = hv = hc/λ and a definite momentum pγ = (h/λ)n, where λ is the wavelength of the incident light (v is its frequency), c is the speed of light, h is Planck’s constant, and n is the unit vector in the direction of propagation of the wave (the subscript γ denotes a photon). In quantum theory the Compton effect appears as an elastic collision between two particles, the incident photon and the stationary electron. In every such collision event the laws of conservation of energy and momentum are obeyed. A photon that has collided with an electron transfers part of its energy and momentum to the electron and changes its direction of motion (it is scattered); the decrease in the photon’s energy signifies an increase in the wavelength of the scattered light. The electron, which previously had been stationary, receives energy and momentum from the photon and is set in motion (it experiences recoil). The direction of motion of the particles after the collision, as well as their energy, is determined by the laws of conservation of energy and momentum (Figure 1). 

Figure 1. 

Note to Figure 1. Elastic collision of a photon and an electron in the Compton effect. Before the collision the electron was stationary: pγ and p’γ are the momentum of the incident and scattered photons, pe = mv 

 is the momentum of the recoil electron (v is its velocity), ( is the photon’s scattering angle, and ø is the angle of escape of the recoil electron relative to the direction of the incident photon. 

Simultaneous solution of the equations expressing the equality of the summed energies and momentums of the particles before and after the collision (assuming that the electron is stationary before the collision) gives Compton’s formula for the shift Δλ in the wavelength of the light: 

Δλ = λ’ − λ = λ0(1 ˗ cos θ) 

Here λ’ is the wavelength of the scattered light, θ is the photon’s scattering angle, and λ0 = h/mc = 2.426 × 10˗10 cm = 0.024 angstrom (Å) is the “Compton wavelength” of the electron (m is the mass of the electron). It follows from Compton’s formula that the shift Δλ in the wavelength does not depend on the wavelength λ of the incident light itself. It is solely determined by the scattering angle θ of the photon and is maximal when θ = 180°, that is, when scattering is straight back: Δλmax = 2λo. 

Expressions for the energy عe of the recoil, or “Compton,” electron as a function of the angle ø of its escape may be obtained from the same equations. The dependence of the energy ع’ γ of the scattered photon on the scattering angle θ, as well as the dependence of عe on ø, which is related to it, is shown in Figure 2. From the figure it is apparent that the recoil electrons always have a velocity component in the direction of motion of the incident photon (that is, ø does not exceed 90°). 

Experiment has confirmed all the above theoretical predictions. The correctness of the corpuscular concepts of the mechanism of the Compton effect—and thus the correctness of the basic assumptions of quantum theory—has been experimentally proved. 

In actual experiments on the scattering of photons by matter, the electrons are not free but are bound to atoms. If the energy of the photons is high in comparison with the binding energy of the electrons in the atom (X-ray and gamma-ray photons), then the electrons experience a recoil strong enough to expel them from the atom. In this case the photon scattering proceeds as if with free electrons. However, if the energy of the photon is not sufficient to tear the electron from the atom, then the photon exchanges energy and momentum with the entire atom. Since the mass of the atom is very great compared to the photon’s equivalent mass (which, according to the theory of relativity, equals £y/c2), the recoil is virtually nonexistent; therefore, the photon 

Figure 2. Dependence of the energy ع’λ of the scattered photon on the scattering angle θ (for convenience, only the upper half of the symmetrical curve is depicted) and the dependence of the energy عe of the recoil electron on the angle of escape 0 (lower half of the curve). Quantities related to the same collision event are labeled with identical numbers. The vectors drawn from point 0, at which the collision between the proton with energy عγ and the stationary electron occurred, to corresponding points on the curves depict the state of the particle after scattering: the magnitudes of the vectors give the energy of the particles, and the angles formed by the vectors with the direction of the incident photon define the scattering angle ø and the angle 0 of the recoil electron’s path. (The graph was plotted for the case of scattering of “hard” X rays with wavelength hc/عγ = γo = 0.024 Å.) 

is scattered without a change in its energy (that is, without a change in its wavelength, or “coherently”). In heavy atoms only the peripheral electrons are weakly bound (in contrast to the electrons filling the inner shells of the atom), and therefore the spectrum of the scattered radiation has both a shifted (Compton) line, from scattering by the peripheral electrons, and an un-shifted (coherent) line, from scattering by the entire atom. With increasing atomic number (nuclear charge) the electron binding energy increases, the relative intensity of the Compton line decreases, and that of the coherent line increases. 

The motion of the electrons in atoms leads to a broadening of the Compton lines in the scattered radiation. This occurs because the wavelength of the incident light appears to be slightly changed for moving electrons; in addition, the amount of change depends on the magnitude and direction of the electron’s velocity (the Doppler effect). Careful measurements of the intensity distribution in a Compton line, which reflects the velocity distribution of the electrons in the material, has confirmed the correctness of quantum theory, according to which electrons obey Fermi-Dirac statistics. 

The simplified theory of the Compton effect examined here does not permit the calculation of all characteristics of Compton scattering, particularly the intensity of photon scattering at various angles. A complete theory of the Compton effect is provided by quantum electrodynamics. The intensity of Compton scattering depends on both the scattering angle and the wavelength of the incident radiation. Asymmetry is observed in the angular distribution of the scattered photons: more photons are scattered forward, and the asymmetry increases with increasing energy of the incident photons. The total intensity of Compton scattering decreases with an increase in the energy of the primary photons (Figure 3); this indicates that the probability of the Compton scattering of a photon passing through matter diminishes with decreasing energy. Such a dependence of intensity on £y determines the place of Compton scattering among the other effects of interaction between matter and radiation that are responsible for loss of energy by photons in their passage through matter. For example, in lead the Compton effect makes the main contribution to the energy loss of photons at energies of the order of 1–10 mega electron volts, or MeV (in a lighter element, aluminum, this range is 0.1–30.0 MeV); below this region it is surpassed by the photoelectric effect, and above it by pair production. 

Compton scattering is used extensively in studying the gamma radiation of nuclei; it is also the basis of the principle of operation of some gamma spectrometers. 

The Compton effect is possible not only for electrons but also for other charged particles, such as protons; however, because of the proton’s large mass its recoil is noticeable only during the scattering of photons with very high energy. 

The double Compton effect consists of the formation of two scattered photons in place of a single incident photon during scattering by a free electron. The existence of this process follows from quantum electrodynamics; it was first observed in 1952. Its probability is approximately a hundred times less than that of the ordinary Compton effect. 

Figure 3. Graph showing the dependence of the total Compton scattering intensity <r on the energy of the photon £y (in units of the total intensity of classical scattering); the arrow indicates the energy at which the production of electron-positron pairs begins 

Inverse Compton effect. If the electrons on which electromagnetic radiation is scattered are relativistic (that is, if they are moving with speeds close to the speed of light), then in an elastic collision the wavelength of the radiation will decrease: the energy and momentum of the photons will increase at the expense of the energy and momentum of the electrons. This phenomenon is called the inverse Compton effect and is often used to explain the radiation mechanism of cosmic X-ray sources, the production of the X-ray component of the background galactic radiation, and the transformation of plasma waves into high-frequency electromagnetic waves. 

Compton effect 

The increase in wavelength of electromagnetic radiation, observed mainly in the x-ray and gamma-ray region, on being scattered by material objects. This increase in wavelength is caused by the interaction of the radiation with the weakly bound electrons in the matter in which the scattering takes place. The Compton effect illustrates one of the most fundamental interactions between radiation and matter and displays in a very graphic way the true quantum nature of electromagnetic radiation. Together with the laws of atomic spectra, the photoelectric effect, and pair production, the Compton effect has provided the experimental basis for the quantum theory of electromagnetic radiation. See Angular momentum, Atomic structure and spectra, Electron-positron pair production, Light, Photoemission, Quantum mechanics, Uncertainty principle 

Perhaps the greatest significance of the Compton effect is that it demonstrates directly and clearly that in addition to its wave nature with transverse oscillations, electromagnetic radiation has a particle nature and that these particles, the photons, behave quite like material particles in collisions with electrons. This discovery by A. H. Compton and P. Debye led to the formulation of quantum mechanics by W. Heisenberg and E. Schrödinger and provided the basis for the beginning of the theory of quantum electrodynamics, the theory of the interactions of electrons with the electromagnetic field. 

The Compton effect has played a significant role in several diverse scientific areas. Compton scattering (often referred to as incoherent scattering, in contrast to Thomson scattering or also Rayleigh scattering, which are called coherent scattering) is important in nuclear engineering (radiation shielding), experimental and theoretical nuclear physics, atomic physics, plasma physics, x-ray crystalloghaphy, elementary particle physics, and astrophysics, to mention some of these areas. In addition the Compton effect provides an important research tool in some branches of medicine, in molecular chemistry and solid-state physics, and in the use of high-energy electron accelerators and charged-particle storage rings. 

The development of high-resolution silicon and germanium semiconductor radiation detectors opened new areas for applications of Compton scattering. Semiconductor detectors make it possible to measure the separate probabilities for Rayleigh and Compton scattering. An effective atomic number has been assigned to compounds that appears to successfully correlate theory with Rayleigh-Compton ratios. 

Average density can be measured by moving to higher energies where Compton scattering does not have to compete with Rayleigh scattering. At these energies, Compton scattering intensity has been successfully correlated with mass density. An appropriate application is the measurement of lung density in living organisms. 

The ability to put large detectors in orbit above the Earth' atmosphere has created the field of gamma-ray astronomy. This field is now based largely on the data from the Compton Gamma-Ray Observatory, all of whose detectors made use of the Compton effect (although not exclusively).  

Max Planck

Max Planck

Max Planck, (born April 23, 1858, Kiel, Schleswig [Germany]—died October 4, 1947, Göttingen, Germany), German theoretical physicist who originated quantum theory, which won him the Nobel Prize for Physics in 1918.

His father received an appointment at the University of Munich, and Planck entered the city’s renowned Maximilian Gymnasium, where a teacher, Hermann Müller, stimulated his interest in physics and mathematics. But Planck excelled in all subjects, and after graduation at age 17 he faced a difficult career decision. He ultimately chose physics over classical philology or music because he had dispassionately reached the conclusion that it was in physics that his greatest originality lay.

His intellectual capacities were, however, brought to a focus as the result of his independent study, especially of Rudolf Clausius’s writings on thermodynamics. Returning to Munich, he received his doctoral degree in July 1879 (the year of Einstein’s birth) at the unusually young age of 21. The following year he completed his Habilitationsschrift (qualifying dissertation) at Munich and became a Privatdozent (lecturer). In 1885, with the help of his father’s professional connections, he was appointed ausserordentlicher Professor (associate professor) at the University of Kiel. In 1889, after the death of Kirchhoff, Planck received an appointment to the University of Berlin, where he came to venerate Helmholtz as a mentor and colleague. In 1892 he was promoted to ordentlicher Professor(full professor). He had only nine doctoral students altogether, but his Berlin lectures on all branches of theoretical physics went through many editions and exerted great influence. He remained in Berlin for the rest of his active life.

Planck recalled that his “original decision to devote myself to science was a direct result of the discovery…that the laws of human reasoning coincide with the laws governing the sequences of the impressions we receive from the world about us; that, therefore, pure reasoning can enable man to gain an insight into the mechanism of the [world]….” He deliberately decided, in other words, to become a theoretical physicist at a time when theoretical physics was not yet recognized as a discipline in its own right. But he went further: he concluded that the existence of physical laws presupposes that the “outside world is something independent from man, something absolute, and the quest for the laws which apply to this absolute appeared…as the most sublime scientific pursuit in life.

The first instance of an absolute in nature that impressed Planck deeply, even as a Gymnasium student, was the law of the conservation of energy, the first law of thermodynamics. Later, during his university years, he became equally convinced that the entropy law, the second law of thermodynamics, was also an absolute law of nature. The second law became the subject of his doctoral dissertation at Munich, and it lay at the core of the researches that led him to discover the quantum of action, now known as Planck’s constant h, in 1900.

In 1859–60 Kirchhoff had defined a blackbody as an object that reemits all of the radiant energy incident upon it; i.e., it is a perfect emitter and absorber of radiation. There was, therefore, something absolute about blackbody radiation, and by the 1890s various experimental and theoretical attempts had been made to determine its spectral energy distribution—the curve displaying how much radiant energyis emitted at different frequencies for a given temperature of the blackbody. Planck was particularly attracted to the formula found in 1896 by his colleague Wilhelm Wien at the Physikalisch-Technische Reichsanstalt (PTR) in Berlin-Charlottenburg, and he subsequently made a series of attempts to derive “Wien’s law” on the basis of the second law of thermodynamics. By October 1900, however, other colleagues at the PTR, the experimentalists Otto Richard Lummer, Ernst Pringsheim, Heinrich Rubens, and Ferdinand Kurlbaum, had found definite indications that Wien’s law, while valid at high frequencies, broke down completely at low frequencies.

Planck learned of these results just before a meeting of the German Physical Society on October 19. He knew how the entropy of the radiation had to depend mathematically upon its energy in the high-frequency region if Wien’s law held there. He also saw what this dependence had to be in the low-frequency region in order to reproduce the experimental results there. Planck guessed, therefore, that he should try to combine these two expressions in the simplest way possible, and to transform the result into a formula relating the energy of the radiation to its frequency.

The result, which is known as Planck’s radiation law, was hailed as indisputably correct. To Planck, however, it was simply a guess, a “lucky intuition.” If it was to be taken seriously, it had to be derived somehow from first principles. That was the task to which Planck immediately directed his energies, and by December 14, 1900, he had succeeded—but at great cost. To achieve his goal, Planck found that he had to relinquish one of his own most cherished beliefs, that the second law of thermodynamics was an absolute law of nature. Instead he had to embrace Ludwig Boltzmann’s interpretation, that the second law was a statistical law. In addition, Planck had to assume that the oscillators comprising the blackbody and re-emitting the radiant energy incident upon them could not absorb this energy continuously but only in discrete amounts, in quanta of energy; only by statistically distributing these quanta, each containing an amount of energy hν proportional to its frequency, over all of the oscillators present in the blackbody could Planck derive the formula he had hit upon two months earlier. He adduced additional evidence for the importance of his formula by using it to evaluate the constant h (his value was 6.55 × 10−27 erg-second, close to the modern value of 6.626 × 10−27 erg-second), as well as the so-called Boltzmann constant (the fundamental constant in kinetic theory and statistical mechanics), Avogadro’s number, and the charge of the electron. As time went on physicists recognized ever more clearly that—because Planck’s constant was not zero but had a small but finite value—the microphysical world, the world of atomic dimensions, could not in principle be described by ordinary classical mechanics. A profound revolution in physical theory was in the making.

Planck’s concept of energy quanta, in other words, conflicted fundamentally with all past physical theory. He was driven to introduce it strictly by the force of his logic; he was, as one historian put it, a reluctant revolutionary. Indeed, it was years before the far-reaching consequences of Planck’s achievement were generally recognized, and in this Einstein played a central role. In 1905, independently of Planck’s work, Einstein argued that under certain circumstances radiant energy itself seemed to consist of quanta (light quanta, later called photons), and in 1907 he showed the generality of the quantum hypothesis by using it to interpret the temperature dependence of the specific heats of solids. In 1909 Einstein introduced the wave-particle duality into physics. In October 1911 Planck and Einstein were among the group of prominent physicists who attended the first Solvay conference in Brussels. The discussions there stimulated Henri Poincaré to provide a mathematical proof that Planck’s radiation law necessarily required the introduction of quanta—a proof that converted James Jeans and others into supporters of the quantum theory. In 1913 Niels Bohr also contributed greatly to its establishment through his quantum theory of the hydrogen atom. Ironically, Planck himself was one of the last to struggle for a return to classical theory, a stance he later regarded not with regret but as a means by which he had thoroughly convinced himself of the necessity of the quantum theory. Opposition to Einstein’s radical light quantum hypothesis of 1905 persisted until after the discovery of the Compton effect in 1922.

Planck was 42 years old in 1900 when he made the famous discovery that in 1918 won him the Nobel Prize for Physics and that brought him many other honours.