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# Week 8a - PHYS142/143 Rm 4.110 Ph 02 42214798 Email...

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PHYS142/143 Rm 4.110 Ph. 02 42214798 Email: [email protected] Wave Particle Duality of Light

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As we have seen, electromagnetic radiation has two aspects, a wave aspect and a particle aspect. Interference and diffraction of e.m. radiation are explained by assuming e.m. radiation consists of waves. Quantum effects, such as the photoelectric and Compton effect are explained by assuming e.m. radiation consists of particle like photons, each photon with energy E and momentum p specified precisely by the frequency, ! , and wavelength, " , of the radiation. ! = E h " = h p (Maxwell predicted e.m. waves also has linear momentum, and that Each equation contains both a wave concept ( ! and " ) and a particle concept (E and p). i.e. Travels as a wave and exchanges energy & momentum as a particle. Note: Any energy-transport phenomenon must be described in terms of waves or of particles, but we cannot simultaneously apply a particle description and a wave description. As we have seen, we only need to use one or other description when considering the properties of light - we can't and never need to use both to explain the same experiment. p = E c = h ! c = h " . )
De Broglie Waves De Broglie suggested in 1924 that since light has a dual wave-particle nature then matter may also have this duality. In analogy with e.m. radiation, de Broglie postulated that the wavelength of a matter wave associated with a particle whose momentum is p would be where m is the relativistic mass of the particle. Note: for an objects " to be large enough to produce observable wave effects, its mass and velocity must be small [see equation], and low speed non relativistic relations may often be used. Because the wave nature of X-rays was verified (in 1912) from diffraction experiments using the atoms of a crystal as an array of diffracting centres, it was quickly recognised that the wave nature of matter could be tested in the same way. Laue X-ray diffraction pattern for quartz crystal.

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e.g. since the typical distance between adjacent atoms is of the order of 0.100 nm, to observe diffraction the electrons wavelength must be comparable and so the K.E. of the electron must be: K.E. = 1 2 m e v 2 = p 2 2m e = 1 2m e h !
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Week 8a - PHYS142/143 Rm 4.110 Ph 02 42214798 Email...

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