Question 2 (3 marks) In a transmission electron microscope a coherent beam of el

Question

Question 2 (3 marks) In a transmission electron microscope a coherent beam of electrons passes through an electrostatic lens, as shown in Figure 2. Inside the first section of the lens (A) the kinetic energy of the electrons is 20 keV. The potential difference between the lens sections A and B is Va -VA - 5kV. Calculate the de Broglie wavelength of the electrons in section B of the lens Hint: You may assume that the mass of the electron is me-9.1 × 10-31 kg. Electron Source S Figure 2: Schematic of an electrostatic lens.

Explanation / Answer

kinetic energy = 1/2mv^2 = 20*10^3*1.6*10^-19 = 32*10^-16 J

debroglie wavelength = h/mv

v = sqrt(2*32*10^-16/9.1*10^-31) = 8.39*10^7 m/s

lambda = 6.63*10^-34/9.1*10^-31*8.39*10^7 = 8.68*10^-12 m

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