The glancing angle (θ) of a Bragg reflection (n = 1) from a set of crystal planes separated by 99.3 pm is 10.42°. Calculate the wavelength of the X-rays that are used in picometers. (1 pm = 10⁻¹² m)
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The Bragg equation for the reflection of radiation of wavelength $\lambda$ from the planes of a crystal is $n \lambda=2 d \sin \theta$ where $d$ is the separation of the planes, $\theta$ is the angle of incidence of the radiation, and $n$ is an integer. Calculate the angles $\theta$ at which X-rays of wavelength $1.5 \times 10^{-10} \mathrm{~m}$ are reflected by planes separated by $3.0 \times 10^{-10} \mathrm{~m}$.
A parallel beam of X-rays is diffracted by a rock salt crystal. The first-order strong reflection is obtained when the glancing angle (the angle between the crystal face and the beam) is $6^{\circ} 50^{\prime}$. The distance between reflection planes in the crystal is $2.8 \AA .$ What is the wavelength of the X-rays? (1 angstrom $=1 \AA=0.1 \mathrm{~nm}$.) Note that the Bragg equation involves the glancing angle, not the angle of incidence. $$ \lambda=\frac{2 d \sin \phi_{1}}{1}=\frac{(2)(2.8 \AA)(0.119)}{1}=0.67 \AA=0.67 \times 10^{-10} \mathrm{~m} $$
X-rays of wavelength 0.0642 nm are scattered from a crystal with a grazing angle of 11.1°. Assume m = 1 for this process. Calculate the spacing between the crystal planes. d = nm
Eduard S.
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