Arthur Holly Compton The Nobel Prize in Physics 1927

biography and work

COMPTON EFFECT

topics
Einstein's photoelectric discussion of 1905 and his other work including "Special Relativity" led physicists to speculate on the "momentum" of these "packets" of light which became known as "photons". Arthur Compton and Debye both provided in 1922 a very simple mathematical framework for the momentum of these photons with Compton having experimental evidence from firing X-Rays of known frequency into graphite and looking at recoil electrons.

Let E = mc2 = hf for a photon, where f is frequency, and "m" is the mass "equivalent" of the photon given they have no "rest mass". (It is important to recognise that stopping a photon to measure its mass eliminates it -so it has no "at rest" mass - crucial in Special Relativity where, to travel at the speed of light, mass would otherwise become infinite.)

Having "rigged" this mass problem,

p = momentum = mc (mass x velocity) = hf /c = E / c = h / l The experiment shows that X-Rays and electrons behave exactly like ball bearings colliding on a table top using the same 2D vector diagrams. They enter the graphite at one wavelength and leave at a longer wavelength as they have transfered both momentum and kinetic energy to an electron. Momentum and energy are conserved in the collision if we accept the equation above for momentum of light.

When the photon enters at l0 and leaves at l1, its energy has changed from E0 to E1 and momentum from E0 / c to E1 / c with a change in direction of q. The electron gains Ek = E0 -E1

Using the cos rule on the diagram above, the energy equation, with some Special Relativity (or by approximation) one can derive the change in wavelength as a function of scattered angle q.

Dl = ( h / mc )( 1 - cosq ) "m" here is the electron mass and the term h / mc is called the "Compton wavelength".

This was corroborated and forced doubting physicists to take the whole photon thing very seriously - which they had not up to this point.



INTRODUCTION

In 1887 discovered the photoelectric effect. Light shone on a piece of metal will eject electrons.

This process appears to conflict classical electromagnetic theory. Light waves which carry energy in the form of oscillating electric and magnetic fields can impart enough energy to an electron so that it is ejected. However, there are features of the photoelectric effect that cannot be described classically.

First, as the intensity of light is increased, the number of ejected electrons increases, but their kinetic energy remains constant. Second, below a certain frequency no electrons are ejected. According to classical theory, if the intensity of the electric and magnetic fields are increased, then these fields will impart more energy to the electrons.

Thus, ejected electrons should have increased kinetic energy. Classical theory stipulates that low frequency light should be able to eject some electrons.

Clearly, classical electromagnetic theory is not adequate to explain this phenomenon. A new theory of light was needed. The work that paved the way for the modern theory of light was begun by Max Planck, who was the first to propose 1 that radiation is not a wave but rather is quantized.

He came to this discovery in his study of black body radiators and determined the formula for the radiative energy density of a black body. But, in order to fit empirical data with his theory, Planck assumed that only discrete amounts of energy could be absorbed or emitted by the black body, in multiples of hf, where h is Planck’s constant and f is the frequency of the radiation. Planck theorized that the composition of the blackbody itself was responsible for the quantization of energy.

In 1905, prompted by Max Planck’s work on black body radiators, Einstein proposed 1 that the energy in an electromagnetic field is not distributed over a wave front but instead localized in clumps or quanta.

The notion that light was a particle and not a wave ran contrary to Maxwell’s equations, that describe light as an electromagnetic wave. However, this new theory explained the photoelectric effect.

According to Einstein, if the intensity of light is increased, the number of photons will increase and thus eject more electrons, but each photon still carries an energy, hf.

Therefore, the kinetic energy of the electrons will remain constant.

The low frequency threshold can also be explained using the particle theory of light. For any metal there is a minimum amount of energy required to remove an electron. Since a photon’s energy is described by hf, below a certain frequency, the photon will not have enough energy to eject an electron. Even though the particle theory of light correctly explains the photoelectric effect, it was not widely accepted.

However in 1923, Arthur Holly Compton provided further evidence that light should be regarded as a particle with energy and momentum.

The photoelectric effect showed that energy is conserved with a collision between a photon and an electron. In the photoelectric effect, the energy of the photon is on the same order of magnitude as the energy binding an electron to a nucleus, a few eV.

Thus, when the photon strikes the electron it imparts only enough energy to eject that electron from the metal. However, if the energy of the photon is large compared to the binding energy of the electron, one could regard the electron as free.

For example, x-ray photons have energy of several KeV. Therefore, both conservation of momentum

and energy could be observed. To show this, Compton scattered x-ray radiation off of a graphite block and measured the wavelength of the x-rays before and after they were scattered. He discovered that the scattered x-rays had a longer wavelength than that of the incident radiation. Compton deduced that if the x-rays were regarded as particles, photons, then he could apply the laws of conservation of energy and momentum to the system. Using these laws he was able to account for and derive the correct expression for the shift in wavelength. Therefore, Compton empirically proved that light can be regarded as a particle.



THEORY

The Compton effect involves scattering high energy photons off of electrons and observing the shift in wavelength between the incident and the scattered photons.

Compton theorized that if photons carry energy, they should also carry momentum.

The energy (E) of a particle is related to its mass (m) and momentum (p), E 2 = pc ( ) 2 + mc 2 ( ) 2 (1) where c is the speed of light. Since the mass of a photon is zero, its energy is E = pc. The energy may also be defined as E = hf , where h is Planck’s constant and f is frequency.

Using these relations, the momentum a photon is related to its wavelength (?), p = h/? .

Compton argued that the shift in wavelength is a result of a single photon imparting momentum to a single electron. Therefore, the theory is derived from the laws of conservation of energy and momentum. Consider a photon with energy E 0 and momentum p 0 , and a stationary electron with rest energy mc 2 .

When the photon collides with the electron, the electron recoils with energy E e and momentum p e .

The scattered photon will have an energy E and momentum p. By conservation of energy and momentum, E e +E = mc 2 + E 0 (2) and p e + p =p 0 (3) Combining energy and momentum conservation using equation (1) yields ? ? ? 0 = h mc 1? cos? ( ) (4)

The shift in wavelength is related only to the mass of the electron and the backscattered angle. The shift has no relation to the energy of the incident photon.

The Compton effect can also be

Arthur Holly Compton was born at Wooster, Ohio, on September 10th, 1892, the son of Elias Compton, Professor of Philosophy and Dean of the College of Wooster. He was educated at the College, graduating Bachelor of Science in 1913, and he spent three years in postgraduate study at Princeton University receiving his M.A. degree in 1914 and his Ph.D. in 1916. After spending a year as instructor of physics at the University of Minnesota, he took a position as a research engineer with the Westinghouse Lamp Company at Pittsburgh until 1919 when he studied at Cambridge University as a National Research Council Fellow. In 1920, he was appointed Wayman Crow Professor of Physics, and Head of the Department of Physics at the Washington University, St. Louis; and in 1923 he moved to the University of Chicago as Professor of Physics. Compton returned to St. Louis as Chancellor in 1945 and from 1954 until his retirement in 1961 he was Distinguished Service Professor of Natural Philosophy at the Washington University. In his early days at Princeton, Compton devised an elegant method for demonstrating the Earth's rotation, but he was soon to begin his studies in the field of X-rays. He developed a theory of the intensity of X-ray reflection from crystals as a means of studying the arrangement of electrons and atoms, and in 1918 he started a study of X-ray scattering. This led, in 1922, to his discovery of the increase of wavelength of X-rays due to scattering of the incident radiation by free electrons, which implies that the scattered quanta have less energy than the quanta of the original beam. This effect, nowadays known as the Compton effect, which clearly illustrates the particle concept of electromagnetic radiation, was afterwards substantiated by C. T. R. Wilson who, in his cloud chamber, could show the presence of the tracks of the recoil electrons. Another proof of the reality of this phenomenon was supplied by the coincidence method (developed by Compton and A.W. Simon, and independently in Germany by W. Bothe and H. Geiger), by which it could be established that individual scattered X-ray photons and recoil electrons appear at the same instant, contradicting the views then being developed by some investigators in an attempt to reconcile quantum views with the continuous waves of electromagnetic theory. For this discovery, Compton was awarded the Nobel Prize in Physics for 1927 (sharing this with C. T. R. Wilson who received the Prize for his discovery of the cloud chamber method).

In addition, Compton discovered (with C. F. Hagenow) the phenomenon of total reflection of X-rays and their complete polarization, which led to a more accurate determination of the number of electrons in an atom. He was also the first (with R. L. Doan) who obtained X-ray spectra from ruled gratings, which offers a direct method of measuring the wavelength of X-rays. By comparing these spectra with those obtained when using a crystal, the absolute value of the grating space of the crystal can be determined. The Avogadro number found by combining above value with the measured crystal density, led to a new value for the electronic charge. This outcome necessitated the revision of the Millikan oil-drop value from 4.774 to 4.803 X 10-10 e.s.u. (revealing that systematic errors had been made in the measurement of the viscosity of air, a quantity entering into the oil-drop method). During 1930-1940, Compton led a world-wide study of the geographic variations of the intensity of cosmic rays, thereby fully confirming the observations made in 1927 by J. Clay from Amsterdam of the influence of latitude on cosmic ray intensity. He could, however, show that the intensity was correlated with geomagnetic rather than geographic latitude. This gave rise to extensive studies of the interaction of the Earth's magnetic field with the incoming isotropic stream of primary charged particles.

Compton has numerous papers on scientific record and he is the author of Secondary Radiations Produced by X-rays (1922), X-Rays and Electrons (1926, second edition 1928), X-Rays in Theory and Experiment (with S. K. Allison, 1935, this being the revised edition of X-rays and Electrons), The Freedom of Man (1935, third edition 1939), On Going to College (with others, 1940), and Human Meaning of Science (1940). Dr. Compton was awarded numerous honorary degrees and other distinctions including the Rumford Gold Medal (American Academy of Arts and Sciences), 1927; Gold Medal of Radiological Society of North America, 1928; Hughes Medal (Royal Society) and Franklin Medal (Franklin Institute), 1940.

He served as President of the American Physical Society (1934), of the American Association of Scientific Workers (1939-1940), and of the American Association for the Advancement of Science (1942). In 1941 Compton was appointed Chairman of the National Academy of Sciences Committee to Evaluate Use of Atomic Energy in War. His investigations, carried out in cooperation with E. Fermi, L. Szilard, E. P. Wigner and others, led to the establishment of the first controlled uranium fission reactors, and, ultimately, to the large plutonium-producing reactors in Hanford, Washington, which produced the plutonium for the Nagasaki bomb, in August 1945. (He also played a role in the Government's decision to use the bomb; a personal account of these matters may be found in his book, Atomic Quest - a Personal Narrative, 1956.)

In 1916, he married Betty Charity McCloskey. The eldest of their two sons, Arthur Allen, is in the American Foreign Service and the youngest, John Joseph, is Professor of Philosophy at the Vanderbilt University (Nashville, Tennessee ). His brother Wilson is a former President of the Washington State University, and his brother Karl Taylor was formerly President of the Massachusetts Institute of Technology. Compton's chief recreations were tennis, astronomy, photography and music. He died on March 15th, 1962, in Berkeley, California.

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