# Wave-particle duality

The wave-particle duality (or particle-wave duality) refers to the double nature of light and matter at the quantum level.

## Contents

The debate arguably began in the 17th century with the competing theories of Christiaan Huygens and Isaac Newton. Huygen's observations led him to a wave theory of light while Newton's observations supported a corpuscular or particle theory. Newton's preeminence as the leading mind in related matters led to the dominance of his theory.

Eventually, subsequent research in the 19th and 20th centuries provided compelling support for both theories—light was found to behave as both a particle and a wave, a characteristic shared by the constituents of solid matter (electrons, atoms and molecules).

Wave theory was strongly supported and continued in optics for more than 100 years. However, in chemistry the atomic structure of matter provided insight into molecular laws of definite proportions. In physics, the atomic theories led to the development of interpretation of numerous properties of solids, liquids and gases including the kinetic theory of gases and the atomic constitution of electricity (e.g. the work of J. J. Thomson in 1899) and H. A. Lorentz’s use of electrons in the theory of interaction of matter with electromagnetic radiation.

Thomas Young's double-slit experiment in 1803[1] strongly indicated that light has wave characteristics. Then in 1924, Prince Louis-Victor de Broglie (1892-1987) presented a hypothesis positing the wave characteristics of particles with small rest mass, such as electrons, and suggested that a wavelength relationship applies to other particles with non-zero rest mass as well.[2] DeBroglie's hypothesis, unequivocally supported by Davisson and Germer's research in 1927 on the diffraction of electron beams by nickel crystals,[3][4] firmly established the wave-mechanics theory underlying current understanding of the wave nature of matter. In 1926, Erwin Schrödinger's (1887-1961) wave equation described the behaviour of electrons and other particles employing wave concepts.

Work on the theoretical basis of the particle nature of radiation received support when the granular structure of light and other types of radiation was confirmed by the discovery of the photoelectric effect:[5] X-rays or light striking solid matter results in the emission of electrons from that matter, showing a direct relationship between the energy of the electrons and the frequency of the incident radiation (the radiation that strikes the solid matter).[6] The subsequent explanation of this phenomenon led to Albert Einstein's theory of light quanta proposed in 1905. In 1922, Arthur Compton observed and reported what is now called the Compton effect, establishing the particle nature of light - photons.[7][8][9][10][11][12][13] In 1927 Dirac quantized the electromagnetic field, thus putting photons (light quanta) on a firm theoretical foundation.

## Example

Wavelengths of various particles with non-zero rest mass according to $\lambda = \frac{h}{mv}$, where λ is the wavelength, h is Planck's constant, m the rest mass, and v the speed of the particle.

 Particle Mass (g) Speed (m/s) Wavelength (pm = 10−12 m) 1 eV electron 9.1× 10−28 5.9× 105 1200 100 eV electron 9.1× 10−28 5.9× 106 120 10,000 eV electron 9.1× 10−28 5.9× 107 12 100 eV proton 1.67× 10−24 1.38× 105 2.9 100 eV α-particle 6.6× 10−24 6.9× 104 1.5 H2 at 200 °C 3.3× 10−24 2.4× 103 82 22-rifle bullet 1.9 320 1.1×10−21 Golf ball 45 30 4.9×10−22 Baseball 140 25 1.9×10−22

From: W. J. Moore, Physical Chemistry, Longmans, London, 2nd edition (1956), p. 271

## References

1. reported in his publication Experiments and Calculations Relative to Physical Optics
2. In his doctoral thesis submitted in 1924 to the Faculty of Sciences at Paris University entitled Recherches sur la Théorie des Quanta (Researches on the quantum theory)
3. Clinton J. Davisson & Lester H. Germer (1927) "Reflection of electrons by a crystal of nickel", Nature, V119, pp. 558-560
4. Davisson-Germer Experiment Dept. of Physics and Astronomy, University of New Mexico. Retrieved April, 20th, 2008
5. The Photoelectric Effect Michael Fowler (1997) University of Virginia. The phenomenon was first observed by J. J. Thomson in 1899 and further demonstrated by Philipp Lenard in 1902, leading to Einstein's theory in 1905
6. The relationship is independent of the intensity of the incident radiation
7. The wave nature of the electron Louise de Broglie (1929) Nobel Lecture
8. Wave-Particle Duality Davisson-Germer Experiment Rod Nave, Department of Physics and Astronomy, Georgia State University
9. Wave-particle duality University of Winnipeg
10. Wave Mechanics Steven S. Wesolowski (1999). Center for Computational Chemistry, University of Georgia, USA
11. The discovery of electron waves Clinton Davisson Nobel lecture, Dec. 13, 1937
12. Louis de Broglie The Nobel Prize in Physics 1929 Nobel Prize Organization
13. Philipp Lenard Biography Nobel Foundation