Question G4.2: X-rays of wavelength 1.45 × 10^-10 m are reflected off a cry...
X-rays of wavelength 1.45 \times 10^{-10} m are reflected off a crystal. When the angle between the X-ray beam and the face of the crystal is increased from zero, a strong reflected beam is detected when the angle becomes 36.4°.
(a) Calculate the spacing of the crystal planes responsible for this reflection.
(b) Are there other angles at which strong reflection is observed?
(a) Using the Bragg condition, we find
\begin{aligned}d &=\frac{n \lambda}{2 \sin \theta} \\&=\frac{1 \times 1.45 \times 10^{-10}}{2 \sin 36.4^{\circ}} \\&=1.22 \times 10^{-10} m\end{aligned}(b) With the value of d just calculated, we have
\begin{aligned}\sin \theta &=\frac{n \lambda}{2 d} \\&=n \frac{1.45 \times 10^{-10}}{2 \times 1.22 \times 10^{-10}} \\&=n \times 0.59\end{aligned}No other angles exist, since for n = 2 or higher we get sinθ > 1, which is impossible.
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