Concept explainers
As a single crystal is rotated in an x-ray spectrometer (Fig. 3.22a), many parallel planes of atoms besides AA and BB produce strong diffracted beams. Two such planes are shown in Figure P3.38. (a) Determine geometrically the interplanar spacings d1 and d2 in terms of d0. (b) Find the angles (with respect to the surface plane AA) of the n = 1, 2, and 3 intensity maxima from planes with spacing d1. Let λ = 0.626 Å and d0 = 4.00 Å. Note that a given crystal structure (for example, cubic) has interplanar spacings with characteristic ratios, which produce characteristic diffraction patterns. In this way, measurement of the angular position of diffracted x-rays may be used to infer the crystal structure.
Figure P3.38 Atomic planes in a cubic lattice.
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Chapter 3 Solutions
Modern Physics
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- The point P(25, 9) lies on the curve y = Vr + 4. If Q is the point (x, Va + 4), find the slope of the secant line PQ for the following values of x. %3D If a = 25.1, the slope of PQ is: and if a 25.01, the slope of PQ is: and if x = 24.9, the slope of PQ is: and if a = 24.99, the slope of PQ is: Based on the above results, guess the slope of the tangent line to the curve at P(25, 9).arrow_forwardPlease answer question e only, thank you. An electron beam is accelerated across a potential difference and on a thinfilm containing crystal fragments that are randomly oriented. The apparatusis like the one we used in the experiment we analyzed this semester, exceptthat the circular ring images are formed on a flat screen, rather than on thesurface of a spherical bulb. All the crystal fragments have the sameinteratomic spacing, dnkl = 0.160 nm. (a) If the accelerating potential difference is 2.8 kV, calculate the electron kinetic energy in eV units.(b) Use the result from (a) to find the electron momentum in Ns units.(c) Use the result from (b) to find the electron wavelength in nm units.(d) Calculate the diffraction angle for the first two orders of Bragg diffraction. Do not use the small angle approximation.(e) The phosphor screen that displays the circular rings is flat and located 22 cm from where the electron beam interacts with the crystal fragments. Calculate the diameters of…arrow_forwardIf A = (x²y)î + (2y3z)j+ (xyz?)k, find the gradient of the divergence of A at the point (-1,1,-2) %3Darrow_forward
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- Solve for 2.1,2.2 and 2.4arrow_forwardConsider a crossbow bolt shot straight upward from the ground (y = 0) at time t = 0 with initial velocity Vo = 47 Take g= 9.8 and p= 0.0013 in cos (C,-t/pg dv Then use the equations v(t) = tan (C,-tvpg) with C, = tan - 1 = -g and y(t)= yo + In to find the maximum %3D dt Vo. cos C, height the bolt reaches. Find the velocity function. v(t) = R (Type an exact answer, using radicals as needed. Do not simplify. Use parentheses to clearly denote the argument of each function.)arrow_forwardEx4@Express W = (x-4) ay in the cylindrical coordinates (b) transform F=f cosa ap in the Cartizian coordinates ?arrow_forward
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