HW7

1. Calculate the wavelength of electrons in a transmission electron microscope for an accelerating voltage of 300 kV both in the non-relativistic and the relativistic limit. (3 points) Calculate also the speed of these electrons in both limits. (2 points)

2. Taking the value of what you think is the correct wavelength of these electrons (from 1), what is the numerical value (in both radian and degrees) of the angle between the transmitted and diffracted electron beam for a crystal’s net-plane spacing of 2 Å. (2 point) Assume Cu Kα radiation and the same net-plane spacing, what would this angle be (in radian and degrees)? (1 point) Would it make sense to reduce the kinetic energy of the primary beam electrons by a factor of 10,000 in a transmission electron microscope to increase this angle so that it can be measured more easily? (1 point) If yes, why. If No, why. (1 point)

3. Is the kinetic energy of the electrons in the primary beam and their linear momentum quantized, in other words does this beam and the microscope form a bound system? (2 points). What quantum mechanical model is applicable to the electrons in the primary beam? (2 points) Is the kinetic energy of the electrons in the diffracted beam and their linear momentum quantized? (1 point)