By D. Hayward
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From the de Broglie relation, the magnitude of the momentum will be h/A, and the component parallel to the surface will therefore be equal to +hsinO/il, the sign depending on whether the particle is diffracted to the left or the right. The uncertainty in the component of momentum parallel to the surface, Apx, will therefore also be equal to hsinO/il. Use of the diffraction relation nil = dsine, with n = 1, leads to Apx = h/d. This is only an approximate formula because the other four first-order diffraction peaks have been ignored, as well as higher-order peaks, but it gives a rough measure of the overall uncertainty in the momentum.
On the other hand, the momentum of the electron is known fairly precisely. 7) Since the value of k can be determined to quite a high accuracy, the uncertainty in the momentum is very small. This is the normal situation with an electron beam, where there is a constant flux of electrons of known energy, but the actual position of individual electrons within the beam is unknown and is of no practical interest. For this situation, Ax is very large and Ap is very small, and the product of the two must be greater than h/2.
Although heavy atoms have wave-like properties, the wavelength is very much shorter than the interatomic distances found in solids, and diffraction is not observed. When electrons or much lighter atoms are used, however, it becomes impossible to give precise trajectories because the wave-like properties of these particles control the scattering. Take electron diffraction, for example. If a beam containing millions of electrons is fired at a nickel target, we know that the diffraction pattern shown earlier will be obtained with six first-order peaks of equal intensity, but it is not possible to know in advance to which spot any particular electron will go.