An electron in a laboratory cathode-ray tube is observed to move at

PHYSICS · Multi-part · A Level · Physics · Particles and radiation · Particles and radiation

Problem

An electron in a laboratory cathode-ray tube is observed to move at 1.50×106 m s−11.50\times10^{6}\,\text{m\,s}^{-1}. Take the electron mass to be 9.11×10−31 kg9.11\times10^{-31}\,\text{kg} and h=6.63×10−34 J sh = 6.63\times10^{-34}\,\text{J\,s}. (a) Calculate the wavelength associated with the electron. (b) The spacing between adjacent planes in a certain crystal is 0.20 nm0.20\,\text{nm}. Would this electron be likely to produce a diffraction pattern when scattered by the crystal? Support your conclusion with a numerical comparison. (c) Determine the ratio of the electron’s speed to the speed of light (c=3.00×108 m s−1c = 3.00\times10^{8}\,\text{m\,s}^{-1}) and comment on the appropriateness of treating the electron as non-relativistic in this calculation.

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