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EE372_Solutions2

EE372_Solutions2 - EE372 Assignment 2 Solutions 1 DeBroglie...

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EE372 Assignment 2 Solutions 1. DeBroglie waves a) Certain scientific installations produce so-called thermal neutrons for neutron diffraction experiments. Such neutrons are in thermal equilibrium with their surroundings so their average kinetic energy is (3 / 2) kT where T is room temperature, 300K. Calculate the average energy (in eV) and the DeBroglie wavelength for a neutron with that energy. Why do you think thermal neutrons are useful for diffraction experiments on materials? The mass of a neutron is 1 . 675 × 10 - 27 kg. b) An electron and a photon both have a wavelength of 500 nm. Calculate the energy (in eV) and the momentum for each. The momentum of a photon is given by h/λ . c) An electron and a photon both have an energy of 1 eV. Calculate the momentum of each. Notice how small the momentum of the photon is compared to the electron. This fact becomes important when light interacts with semiconductors and has consequences for the electronics industry. d) The resolving power of a microscope (that is the smallest detail that can be observed) is about equal to the wavelength used. If one wanted to “see” atoms (of size 0.05 nm) in a “light” microscope, what energy photons are required (in eV)? If instead one used an electron microscope to image atoms, what accelerating potential is required to give the electrons the needed wavelength? (Actual electron microscopes use much larger potentials for technical reasons.) e) High energy physics experiments use sub-atomic particles accelerated to very high energy to probe the structure of other particles. If an electron is accelerated to 50 GeV, what is its wavelength? For highly relativistic particles, the momentum is related to energy by p = E/c .

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