When scattering x-rays with a wavelength of 3.28 × 10^-10 m from a crystal, the first interference maximum occurs at an angle of 23.0 degrees relative to the crystal surface. What is the crystal spacing? A) 4.2 × 10^-10 m B) 16.8 × 10^-10 m C) 6.3 × 10^-10 m D) 8.4 × 10^-10 m

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Quizplus · Accepted Answer

The crystal spacing can be calculated using Bragg's law, $n\lambda = 2d\sin(\theta)$, where $n$ is the order of the maximum (here, $n=1$ for the first maximum), $\lambda$ is the wavelength of the x-rays, $d$ is the crystal spacing, and $\theta$ is the angle of incidence (or diffraction). Rearranging for $d$, we get $d = \frac{\lambda}{2\sin(\theta)}$. Substituting $\lambda = 3.28 \times 10^{-10} \, \text{m}$ and $\theta = 23.0$ degrees into the equation gives a crystal spacing of approximately $4.2 \times 10^{-10} \, \text{m}$.

When Scattering X-Rays with a Wavelength of 3