Davisson and Germer experiment
Bearing in mind that the kinetic energy of the electrons is given by ½mv 2 = Ve and that the wavelength associated with them is h/mv, the wavelength is given by λ = h/√(2Vem). Substitution of relevant data gives
λ = (6.6 × 10-34/√(2 × 54 × 1.6 × 10-19 × 9.1 × 10-31) = 1.67 × 10-10 m = 0.167 nm.This wavelength is in the X-ray range. X-rays had already provided information about the spacing of the atomic planes in the nickel crystal, and it is therefore a simple matter to use the Bragg formula (see Bragg's law) to calculate the wavelength of the scattered electrons. As the angle of scattering is 5o°, the angles of incidence and reflection must each be 25°. This implies that the reflecting planes in the crystal are inclined at 25° to the top surface of the crystal. The distance d between the reflecting crystal planes is d = 215 sin 25° = 90.9 pm. Using the Bragg formula mλ = 2d sin θ we get &lambda = 2 × 90.9 sin 65° = 165 pm. Agreement between the measured and predicted wavelength is therefore established.
Related category ATOMIC AND NUCLEAR PHYSICS
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