Question

The first-order diffraction maximum is observed at 11.70 for a crystal having an interplanar spacing of 0.290 nm. How many other orders can be observed in the diffraction pattern? Your response differs from the correct answer by more than 10%. Double check your calculations, orders At what angles do they appear? (Enter NONE in any unused answer blanks.) m = 2 appears at m = 3 appears at m = 4 appears at m = 5 appears at Why is there an upper limit to the number of observed orders?

Answer 1

Solutim C. Given b that r. for the first order maximum G= interplanar spacing, d = 0.2gonm = 0.29x109 m from, Bragg's law of diffraction, we can write 2d sin 6 = nn ar d = Rasino - 2x0.294159 sin 11.7 For = 1.176x10-10m m=2, 2 d sina = md or, sino = ma or = sin (2x 1.176x10-10) 2d or o = sin- (2^2 x 0.29x109) or, O = 23.92 For m=2 appears at 23.920. for m=3 o = sintl (mn 2d = sin / 3 x 1.176x10-10 ( 2 x 0.29 X 10^9 - 37.46° om m=3 appears at 37.46.

For m = 4 . o = sint (md) = sin(4x1.176 810-10) ( 2x0.290 x 10-9 er 0 = 54.19°. m= 4 appears at 54.19°. For for m=5 e = sin-i (mA) on @ = sin-'(5 x1176 10-10 2 x 0.290 X 1093 ar, 0 = invalid. Here, the upper limit is 4. Because the value of sing can be never be greater than I.