If an X-ray with a wavelength of 185 pm is diffracted at an angle 2$\theta$=16.9, according to the Bragg equation (n$\lambda$ =2 d sin$\theta$), what is the distance between layers of the crystal that give rise to this diffraction? Assume n= 1 in this problem.

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Quizplus · Accepted Answer

The Bragg equation is $n\lambda = 2d\sin(\theta)$, where $n$ is the order of diffraction (assumed to be 1 in this problem), $\lambda$ is the wavelength of the X-ray, $d$ is the distance between layers in the crystal, and $\theta$ is the angle of diffraction. Given $\lambda = 185$ pm and $\theta = 16.9^\circ$, we can solve for $d$:$$d = \frac{\lambda}{2\sin(\theta)} = \frac{185}{2\sin(16.9^\circ)} \approx 629.4 \text{ pm}$$

If an X-Ray with a Wavelength of 185 Pm Is θ\thetaθ

If an X-Ray with a Wavelength of 185 Pm Is $\theta$