An electron beam in a laboratory experiment travels in vacuum with a speed of (well…

PHYSICS · Multi-part · CBSE · Physics · Dual Nature of Radiation and Matter · Dual Nature of Radiation and Matter

Problem

An electron beam in a laboratory experiment travels in vacuum with a speed of 2.0×106 m s−12.0\times10^{6}\,\text{m s}^{-1} (well below the speed of light c=3.0×108 m s−1c = 3.0\times10^{8}\,\text{m s}^{-1}). (i) Calculate the speed of the electrons as a percentage of the speed of light. (ii) Treating the electrons as non-relativistic, determine the de Broglie wavelength associated with the beam. (iii) Express the wavelength obtained in part (ii) in ångström (1 A˚=10−10 m)(1\,\text{Å} = 10^{-10}\,\text{m}) and comment whether it lies in the X-ray region of the electromagnetic spectrum.

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