A transmission electron microscope (TEM) forms an image by sending a beam of fas

Question

A transmission electron microscope (TEM) forms an image by sending a beam of fast-moving electrons rather than a beam of light through a thin sample. According to De Broglie's Hypothesis of quantum mechanics, such fast-moving electrons behave pretty much like a light wave, with wavelength inversely proportional to the momentum (and hence to the speed) of the electrons. Thus, if the electrons have sufficiently high speed, their wavelength will be comparable to the size of an atom. On the other hand, the wavelength of visible light is about a thousand times greater than the size of an atom. Hence, the sufficiently fast electrons of a TEM can form image's which show much finer detail than even the best optical microscope. In a TEM, the electrons are emitted from a heated metal filament and are then accelerated toward another piece of metal called the anode that is at a potential of 2.5 kV (1 kV = 1 kilo Volt 10^3 V) higher than that of the filament. Fig. 1.1. If the electrons leave the filament initially at rest, how fast are the electrons moving when they pass through the anode?

Explanation / Answer

Kinetic energy of the electron = qV

0.5mv^2 = qV

0.5*9.11*10^-31*v^2 = 1.6*10^-19*2500

v = 2.96*10^7 m/s

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