A beam of electrons with kinetic energy 350 eV is incident normal to the surface of a KC1 crystal that has been cut so that the spacing d between adjacent atoms in the planes parallel to the surface is 0.315 nm. (a) There are multiple diffraction peaks from this scattering corresponding to different inte- gers n in the Bragg condition. Show that there is a maximum n above which diffraction peaks are not possible, and find this integer nmax. (b) Calculate the angles at which diffraction peaks will occur for all orders that are possible.
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- Estimate the wavelength and energy (in eV) of a photon with which one can resolve featuresof a sample that are 0.1 nm in size. Assume that in order to resolve a feature, the wavelength mustbe smaller than the size of the feature.(b) Estimate the wavelength and energy (in eV) of an electron with which one can resolve featuresof a sample that are 0.1 nm in size. Again, assume that in order to resolve a feature, thewavelength must be smaller than the size of the featConsider scattering with electrons of 54 eV on a crystal with planes separated by 0.22 nm. How many diffraction peaks should be expected? Justify your answerA one-dimensional square well of infinite depth and 1 Å width contains 3 electrons. The potential well is described by V = 0 for 0 1 Å. For a temperature of T = 0 K, the average energy of the 3 electrons is E = 12.4 cV in the approxination that one neglects the Coulomb interaction between clectrons. In the same approximation and for T = 0 K, what is the average cuergy for 4 electrons in this potential well?
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- Q2 A slab of diefectric materials haş electri susceptrbility Xe=15 the electric freld intensity '(inside the dielectri)-is: E=150 X ax + 2y ay Vt Fiind (tuside the dietectric): Jant ) dielectvic constant, ii) Po at P(3+1,4) (the pointisinside the dieleetrie ¥) tvAn arbitrary quantm mechanical system is initially in the ground state |0). At t = 0, a perturbation of the form H' (t) = Hoc:/T is applied. Show that at large times the probability that. tlhe system is in state |1) is given by |(0}Ho|1}|2 (A) A + (Ac)? where As is the difference in cnergy of states |0) and |1). Be specific about what assumption, if any, were inade arriving at your conclusion.pls answer d and e
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