# 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-centred 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-centred 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.