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- pls show all steps 1) Assume that the elemental atoms are hard spheres of radius r.Calculate the maximum packing rate t obtained when this elementcrystallizes into the following structures:(a) simple cubic (sc)(b) body-centered cubic (bcc)(c) face-centered cubic (fcc)Next nearest neighbor interactions. Consider a monatomic lattice. The potential energy of the crystal system, modeled as a linear chain of atoms is UpE. = 1/(2 a)E„x? where n runs over all the atoms in the chain and x, is the net displacement of the n'th atom. (a) Show that if the atom is interacting with p atoms on either side instead of one (as we discussed in class), the the force acting on the n'th atom is given by, Fn -Eap(un – Un+p); +p where a, represents the force constant between atoms numbered n and n+ p. (b) Let's now consider an atom interacting with four neighboring atoms, two on each side (i.e., p = 2). If a and m have the usual meanings, show that the dispersion relation is given by, 4a sin? (등) (1+ 4 cos? (등)). qa qa w? тNow assume that both the H and the I move when the molecule rotates so the rotating HI moleculeis a rigid rotator and calculate: c) the rotator’s moment of inertiad) the greatest wavelength of radiation that can rotationally excite the molecule.
- Using the following ionic radii, calculate the void volume fraction in the CsCl. Assume that the ions are practically spherical. Note: Establish the ratios of the radii from the Pythagorean theorem and explain the development steps. -Answers a = 4.04 ÅVoid = 0.317For a material having FCC crystal cell structure, write the expressions for Planar atomic density in planes (0,0,1) and (1,1,0) in terms of atomic radius ‘r’ and calculate for Copper in gms/cm3 . Why metal shows directional nature of properties at atomic level whereas its bulk measured properties are isotropic in nature.Using the following ionic radii, calculate the void volume fraction in LICI. assume that the ions are practically spherical. lon Radio, A Li 0.6 1.81
- 1) Let us consider GaAs structure with lattice constant a (look it up from the book) a) How many nearest neighbor atoms (As) of a Ga in unit cell? b) Calculate nearest neighbor distance in nm. c) How many atoms (specify type) sits on top surface of a 4 section (cubic) of Ga unit cell d) What is the Ga atomic density in (110) plane?Find the repulsive exponent n. Given: nearest neighbour equilibrium distance, R0 = 3.14 Å, compressibility of KCl, K = 5.747 x 10–11 m2/N and Madelung constant M = 1.748. please write on a paperHcp structure. Show that the cla ratio for an ideal hexagonal close-packed strue- ture is 2 = 1.633. If cla is significantly larger than this value, the crystal structure be thought of as composed of planes of closely packed atoms, the planes being loosely stacked. %3D may
- help me solve pls....pls prioritize (b)1. Singularity in density of states. (a) From the dispersion derived in Chapter 4 for a monatomic linear lattice of N atoms with nearest neighbor interactions, show that the density of modes is D(w) = m where is the maximum frequency. (b) Suppose that an optical phonon branch has the form @(K) = @- AK², near K = 0 in three dimension. Show that for @@. Here the 2N 1 π (@²-0²) 1/2" m L 2π - (2-) - 250 (0 (@-@)¹/² 2π D(@) = density of modes is discontinuous.P9E.11 (a) For a linear conjugated polyene with each of N carbon atoms contributing an electron in a 2p orbital, the energies E, of the resulting A molecular orbitals are given by: E, =a+2B cos- N+1 k=1, 2,.,N Use this expression to make a reasonable empirical estimate of the resonance integral B for the homologous series consisting of ethene, butadiene, hexatriene, and octatetraene given that t-n ultraviolet absorptions from the HOMO to the LUMO occur at 61 500, 46 080, 39 750, and 32 900 cm", respectively. (b) Calculate the T-electron delocalization energy, Egdo:= E, - n(a+ B), of octatetraene, where E, is the total T-electron binding energy and n is the total number of T-electrons. (c) In the context of this Hückel model, the molecular orbitals are written as linear combinations of the carbon 2p orbitals. The coefficient of the jth atomic orbital in the kth molecular orbital is given by: cN sin j=1,2.N jkn j=1, 2,.,N Evaluate the coefficients of each of the six 2p orbitals in each…