A beam of x-rays whose wavelegth is 0.03875 nm impinges on acrushed crystal pack

Question

A beam of x-rays whose wavelegth is 0.03875 nm impinges on acrushed crystal packet with a single interplane separationof d nm. A sheet of film lies normal to the x-ray beam, adistance 50 cm from the crushed crystal. The first scatteringmaximum (Bragg peak) forms a circle of radius 20 cm as shown in thefigure below. Only the smallest radius circle is shown.

A view of the scattering at the atomic level is shownschematically in the figure below.

a) Calculate the distance between Bragg scattering planes.
d = nm    

b) Find the maximum number of Bragg peaks which could appear onthe film plane even if it had infinite extent.

Number of Bragg Peaks =     

c) Find the minimum radius of the film plane necessary tocontain the largest radius Bragg peak computed in part b.

rmin = cm    

d) Find the longest wavelength x-ray that will produce a Braggpeak on a sheet of film of the radius found in part c for theinterplane separation found in part a.

Explanation / Answer

a)The distance between Bragg scattering planes 2d * sin = m * m =1,2,3,.............. or d = (m * /2sin) -----------(1) m = 1, = 0.03875 nm = 0.03875 * 10-9 m and = 90o b)The maximum number of Bragg peaks which could appear on thefilm plane even if it had infinite extent N = (1/d) c)The minimum radius of the film plane necessary to containthe largest radius Bragg peak computed in part b rmin = (m * * D/d) D = 50 cm = 50 * 10-2 m and the value of d isobtained from equation (1) (d)The longest wavelength x-ray that will produce a Bragg peakon a sheet of film of the radius found in part c for the interplaneseparation found in part a is max = (2d * sin/m) m = 1 and = 90o b)The maximum number of Bragg peaks which could appear on thefilm plane even if it had infinite extent N = (1/d) c)The minimum radius of the film plane necessary to containthe largest radius Bragg peak computed in part b rmin = (m * * D/d) D = 50 cm = 50 * 10-2 m and the value of d isobtained from equation (1) (d)The longest wavelength x-ray that will produce a Bragg peakon a sheet of film of the radius found in part c for the interplaneseparation found in part a is max = (2d * sin/m) m = 1 and = 90o

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