# Worksheet: Bragg's Law

In this worksheet, we will practice derive Bragg's law and use this formula to calculate lattice spacings, scattering angles, and radiation wavelengths.

Q1:

When an electron in an excited atom of molybdenum relaxes from the L-shell to the K-shell, an X-ray photon is emitted. Diffraction of this light by layers of atoms 2.64 Å apart produces a first-order reflection at . Calculate the difference in energy between the L- and K-shells of the molybdenum atom.

Q2:

X-rays of wavelength 0.5594 Å are diffracted by a face-centered cubic metal lattice. The radius of the metal atom is 1.345 Å. Calculate to, 3 significant figures, the diffraction angle of the second-order reflection ().

Q3:

Platinum crystallizes with a face-centered cubic unit cell and diffracts X-rays of wavelength 1.541 Å to produce a second-order () reflection at . Calculate to 3 significant figures the density of platinum.

Q4:

X-rays of wavelength 0.2879 nm are diffracted by a crystal with a layer spacing of 4.164 Å. Calculate to 3 significant figures the diffraction angle of the first-order reflection.

Q5:

When X-rays of wavelength 0.2287 nm are diffracted by a crystal, the first-order reflection occurs at angle . Calculate to 3 significant figures the spacing of the crystal planes that give rise to this reflection.

Q6:

When X-rays of wavelength 1.541 Å are diffracted by a crystal, the first-order reflection occurs at angle . Calculate to 3 significant figures the spacing of the crystal planes that give rise to this reflection.

Q7:

X-rays of wavelength 1.936 Å are diffracted by a body-centered cubic metal lattice. The radius of the metal atom is 1.260 Å. Calculate the diffraction angle of the second-order () reflection in degrees to 3 significant figures.

Q8:

X-rays of wavelength 0.1057 nm are diffracted by a cubic metal lattice, producing a second-order () reflection at . The metal atom has a radius of 1.680 Å and molar mass of 210 g/mol. Calculate the density of the metal to 3 significant figures.