X-ray diffraction: If an X-ray beam of wavelength 1.4 × 10^-10 m makes an angle of 30° with a set of planes in a crystal causing first order constructive interference, what is the plane spacing? A) 0.28 nm B) 0.070 nm C) 0.32 nm D) 0.16 nm E) 0.14 nm

Question

Quizplus · Accepted Answer

Using Bragg's law, $n\lambda = 2d\sin\theta$, where $n=1$ (first order), $\lambda = 1.4 \times 10^{-10} m$ (wavelength), and $\theta = 30°$. Solving for $d$ (plane spacing), $d = \frac{\lambda}{2\sin\theta} = \frac{1.4 \times 10^{-10}}{2\sin(30°)} = \frac{1.4 \times 10^{-10}}{2 \times 0.5} = 1.4 \times 10^{-10} m = 0.14 nm$.

X-Ray Diffraction: If an X-Ray Beam of Wavelength 1