X-rays of wavelength 1.45 × 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

Question

X-rays of wavelength [latex]1.45 imes 10^{-10} m[/latex] 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?

Accepted Answer

(a) Using the Bragg condition, we find

[latex]\begin{aligned}d &=\frac{n \lambda}{2 \sin heta} \&=\frac{1 imes 1.45 imes 10^{-10}}{2 \sin 36.4^{\circ}} \&=1.22 imes 10^{-10} m\end{aligned}[/latex]

(b) With the value of d just calculated, we have

[latex]\begin{aligned}\sin heta &=\frac{n \lambda}{2 d} \&=n \frac{1.45 imes 10^{-10}}{2 imes 1.22 imes 10^{-10}} \&=n imes 0.59\end{aligned}[/latex]

No other angles exist, since for n = 2 or higher we get sinθ > 1, which is impossible.

Question G4.2: X-rays of wavelength 1.45 × 10^-10 m are reflected off a cry...

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