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Background

Wave–particle duality is an ongoing conundrum in modern physics. Most physicists accept wave-particle duality as the best explanation for a broad range of observed phenomena; however, it is not without controversy.

This article discuss how the compton effect proved that the light could be observed as  particles and that the wave theory has failed in explaining the behaviour of light in all manners.

Introduction

The duality about the nature of light has been there for a long time, but the ideas about the nature of light has been the topic for discussion even before that duality existed. "Aristotle was one of the first to publicly hypothesize about the nature of light, proposing that light is a disturbance in the element aether (that is, it is a wave-like phenomenon). On the other hand, Democritus—the original atomist—argued that all things in the universe, including light, are composed of indivisible sub-components (light being some form of solar atoms)" [6].

At the beginning of the 11th Century, the Arabic scientist Alhazen wrote the first comprehensive treatise on optics,  describing refraction, reflection, and the operation of a pinhole lens via rays of light traveling from the point of emission to the eye. He asserted that these rays were composed of particles of light.

The modern duality about the nature of light starts from Huygens - Newton duality about the nature of light, "when Christiaan Huygens and Isaac Newton proposed competing theories of light: light was thought either to consist of waves (Huygens) or of particles (Newton)" [6].

Huygens and Newton

Newton was interested in light from very early on in his career, the work that first brought him to the attention of the scientific community was his experimental investigation of colour, and his invention of the ‘Newtonian’ reflecting telescope (published in 1672). However this work provided no theory of how light worked, and Newton made attempts at this for many years. For various reasons he favoured a particle theory of light – the explanation of light propagating in straight lines, except at interfaces, was then easily understood. Still, light particles were acted upon by an invisible aether.

However Huyghens on the other hand thought of light as a wave, his most important contribution to science by far was his wave theory of light. He demonstrated how waves might interfere to form a wavefront, propagating in a straight line. He argued that the known properties of light, such as refraction, reflection and propagation in straight lines, could be understood by assuming that light was a wave in some invisible medium, analogous to waves moving in a fluid. Refraction could be understood if the waves traveled more slowly in a dense medium (like waves in shallow water).

He gave the first theory of wave propagation, showing, among other things how they could be built up from ‘elementary wavelets’, radiated in circular patterns from multiple sources.

Compton

Although Max Planck and Albert Einstein postulated that light could behave as both a wave and a particle, it was Arthur Compton who finally proved that this was possible. His experiment involved scattering photons off electrons and offered proof for what we now refer to as the Compton effect.

The compton effect (also known as compton scattering) is the result of a high-energy photon colliding with a target, which releases loosely bound electrons from the outer shell of the atom or molecule.

The Compton effect was observed by Arthur Compton in 1922, by observing the "scattering of x-rays from electrons in a carbon target, and finding scattered x-rays with a longer wavelength than those incident upon the target. The shift of the wavelength increased with scattering angle according to the Compton formula:



Compton explained and modeled the data by assuming a particle (photon) nature for light and applying conservation of energy and conservation of momentum to the collision between the photon and the electron. The scattered photon has lower energy and therefore a longer wavelength according to Planck’s relationship" [8].

By that time the photoelectric effect suggested that light consisted of particles was really debated.

The compton's original experiment made use of molybdenum K-alpha x-rays, which have a wavelength of 0.0709 nm. These were scattered from a block of carbon and observed at different angles with a Bragg spectrometer. The spectrometer consists of a rotating framework with a calcite crystal to diffract the x-rays and an ionization chamber for detection of the x-rays. Since the spacing of the crystal planes in calcite is known, the angle of diffraction gives an accurate measure of the wavelength.

Figure 1. Compot Experiment.


By Compton observation, after the scattering the frequency (energy) of the x-rays had changed, and had always decreased. From the point of view of classical (wave) electromagnetic theory, this frequency shift cannot be explained since the frequency is a property of the incoming electromagnetic wave and cannot be altered by the change of direction implied by the scattering.

If, on the other hand, the incoming radiation is thought of as a beam of photons (electromagnetic quanta) then the situation becomes that of photons of energy

E = hv.

scattering from free electrons in the target material. Energy-momentum conservation, applied to this situation, predicts that the scattered photons will have an energy of:

E' = hv' <E.

in complete agreement with Compton’s experiments.

The frequency shift will depend on the angle of scattering, and can be calculated from kinematics. Consider an incoming photon of energy hv and momentum hv/c scattering from any electron of mass m. p is the momentum of the electron after scattering and hv', hv'/c are the energy and momentum of the scattered photon.
For momentum conservation, the three vectors hv/c, hv'/c and p must lie in the same plane.




Figure 2. Compton scattering diagram showing the relationship of the incident photon and electron initially at rest to the scattered photon and electron given kinetic energy.

This what actually led to the compton formula.

" Compton and his coworkers realized the classical wave theory of light failed to explain the scattering of X-rays from electrons. According to classical mechanics, electromagnetic waves of frequency f0, incident on electron should have two effects:

  1. Radiation pressure should cause acceleration of electrons in the direction of the radiation.

  2. The oscillating field of X-ray should set electrons in oscillation at frequency f`, where f`is the frequency in the frame of the moving electron.

The apparent frequency f`of the electron is different than f0 because of the Doppler’s effect. Each electron first absorbs radiation as a moving particle and then reradiates as a moving particle, thereby exhibiting two Doppler shifts in the frequency of radiation. Because different electrons move at different speeds after the interaction, depending on the amount of energy absorbed from the incident electromagnetic waves, scattered wave frequency should show a distribution of Doppler shifted value in relation to angle of approach." [3].

According to the quantum electron particle model this observation is not correct. We believe electrons in orbit shall absorba precise quantum of energy from EM-wave and re-radiate by precise amount by processes described by us, selective absorption and emission. We shall ignore quantum particle description for the time being. Contrary to see distribution, Compton discovered that at a given angle of approach only one frequency of radiation is observed in scattered spectrum. Compton explained this observation by stating that the EM waves were behaving like photon particles having energy hf and momentum hf/c. ating in a straight line. However, the theory had difficulties in other matters, and was soon overshadowed by Isaac Newton's corpuscular theory of light. That is, Newton proposed that light consisted of small panation.

After the observation of the compton effect it was clear to scientist that light could be observed in both ways (as particles and as waves).

Reference:

  1. Compton, Arthur H. “ A Quantum Theory Of the Scattering of X-Rays by Light Elements.” Physical Review Phys. Rev. 21, no. 5 (1923): 483–502. doi:10.1103/physrev.21.483 

  2. Dr. James E. Parks. “The Compton Effect-- Compton Scattering and Gamma Ray Spectroscopy” Department of Physics and Astronomy 401 Nielsen Physics Building The University of Tennessee Knoxville, Tennessee 37996-1200. Revision 3.00 (January 6, 2015).

  3. Shailesh R. Kadakia, “Revolution; Light is a wave: Revisiting the outcome of light’s particle nature experiments”: 13-18.

  4. “Compton Scattering.” Wikipedia. Wikimedia Foundation. Accessed May 15, 2015. http://en.wikipedia.org/wiki/compton_scattering.

  5. “Light.” Wikipedia. Wikimedia Foundation. Accessed May 16, 2015. http://en.wikipedia.org/wiki/light.

  6. “Wave–Particle Duality.” Wikipedia. Wikimedia Foundation. Accessed May 15, 2015. http://en.wikipedia.org/wiki/wave–particle_duality.

  7. “Light.” Wikipedia. Wikimedia Foundation. Accessed May 15, 2015. http://en.wikipedia.org/wiki/light.

  8. “Compton Scattering.” Compton Scattering. Accessed May 15, 2015. http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/comptint.html.

 


By Abdulla Ibrahim. Created 15/05/2015. Last edition 16/05/2015.

Modern Physics, spring 2015

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