Matter Waves

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Radiation has dual nature: it behaves as a wave in some phenomena and as a particle in others. Interference, diffraction, and polarisation are explained by wave nature, while photoelectric effect and …

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Different experiments need different models. Wave nature explains interference, diffraction, and polarisation. Particle nature explains photoelectric effect and Compton effect. The wave picture suits …

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Radiation is emitted not continuously but in small bundles or packets of energy called photons.

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Photon energy: E = h v. Photon momentum: p = h v / c. Here h is Planck's constant, v is frequency, and c is the speed of light.

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A photon has energy E = h v, kinetic mass = h v / c^2, momentum p = h v / c, speed c, and zero rest mass. It is electrically neutral and is not deflected by electric or magnetic fields.

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Total energy and total momentum remain conserved. The number of photons may not be conserved because a photon may be absorbed by matter and a new photon may be created.

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Given: λ = 500 nm = 500 x 10^-9 m = 5.0 x 10^-7 m. Formula: p = h / λ. Using h = 6.63 x 10^-34 J-s, p = (6.63 x 10^-34) / (5.0 x 10^-7) = 1.326 x 10^-27 kg m s^-1. Answer: p ≈ 1.33 x 10^-27 kg m s^-1.

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Given: v = 6.0 x 10^14 Hz. Formula: E = h v. Using h = 6.63 x 10^-34 J-s, E = (6.63 x 10^-34) x (6.0 x 10^14) = 3.978 x 10^-19 J. Answer: E ≈ 3.98 x 10^-19 J.