Module 5 : MODERN PHYSICS
Lecture 26 : Wave Nature of Particle - the de Broglie Hypothesis
  Example 15
One of the diffraction peaks observed by Davisson and Germer for a 65 keV electron beam was at a direction such that the angle between the incident beam and the scattered beam is 60 $ ^\circ$. For what value of crystal spacing is this peak seen in the first order ?
  Solution :
For $ \phi=60^\circ$, the angle $ \theta=30^\circ$. A kinetic energy of 65 keV corresponds to $ K=65\times 10^3\times 1.6\times 10^{-19}= 1.04\times 10^{-14}$J. Equating this to $ p^2/2m$, the momentum $ p= \sqrt{2mK}= 1.39\times 10^{-22}$ kg-m/s. The wavelength corresponding to this momentum is $ h/p = 4.76\times 10^{-12}$ m. The crystal spacing is given by
 
$\displaystyle d = \frac{\lambda}{2\sin\theta}= 4.76\times 10^{-12}\ \ {\rm m}$

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