(Solved): 7. Diatomic line. Consider a line of atoms ABABAB, with an AB bond length of a1a. The ...

7. Diatomic line. Consider a line of atoms $$ABAB\dots AB$$, with an $$A?B$$ bond length of $$\frac{1}{a}a$$. The form factors are $$f_A,f_B$$ for atoms $$A,B$$, respectively. The incident beam of x-rays is perpendicular to the line of atoms. (a) Show that the interference condition is $$n?=a\cos ?$$, where $$?$$ is the angle between the diffracted beam and the line of atoms. (b) Show that the intensity of the diffracted beam is proportional to $${?f_A?f_B?}^2$$ for $$n$$ odd, and to $${?f_A+f_B?}^2$$ for $$n$$ even. (c) Explain what happens if $$f_A=f_B$$.