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a) Figure 4 shows the reflection of two rays of radiation from consecutive planes with spacing
d, where θ is the angle of incidence as shown. Explain why constructive interference occurs
if the following condition is obeyed:
2d sin θ = λ,
where λ is the wavelength of the radiation.
d) Table 1 shows a set of measured values for angles 2θ at which peaks in scattered radiation
are observed, where λ = 1.4 A is the wavelength of the radiation.
(i) Fill in the second column of the table, showing squared plane spacings (in units of A˚2)
corresponding to the measured deflection angles.
(ii) Fill in the third column, where d0 is the plane spacing corresponding to the first entry
in column 2.
(iii) Find an integer N in the final column of the table, that makes all entries an integer.
Transcribed Image Text:8
20
2
d
Figure 4: Reflection of radiation from two consecutive planes.
20/⁰ ď² = (A/2 sin 0)² | ²/ď² | NŒ²/ď²
34.733
40.322
58.342
69.716
73.305
Table 1: Diffraction analysis for titanium carbide.
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