Particles as waves. Particles as waves. Aims understand that electron diffraction is evidence for wave-like behaviour use the de Broglie equation
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Particles as waves
Diffractionreview - conclusions
The de Broglie equationIn 1923 Louis de Broglie proposed that a particle of momentum p would have a wavelength λ given by the equation:
2. Find the wavelength of a cricket ball of mass 0.15 kg moving at 30 m s-1.l = h/p = [6.63 ´ 10-34] / [0.15 ´ 30] = 1.47´10-34 m = 1.5 10-34 J s (to 2 s.f.)This is a very small number, and explains why a cricket ball is not diffracted as it passes near to the stumps.
Calculate the wavelength of an electron accelerated through a potential difference of 10 kV.
Step 1: Kinetic energy Ek = eV = 1.6 ´ 10-19 ´ 10000 = 1.6 ´ 10-15 J
Step 2: EK = ½ mv2 = ½m (mv) 2 = p2 / 2m,
so momentum p = √2mEk = √2 x 9.1 x 10-31 x 1.6 ´ 10-15 = 5.4 x 10-23 kg m s-1
Step 3: Wavelength l = h / p = 6.63x10-34 / 5.4 x10-23 = 1.2 x 10-11 m = 0.012 nm.