A spherical grain of dust

PHYSICS · Multi-part · Fermi University Physics · Condensed Matter, Materials & Soft Matter · Lattice dynamics and thermal properties of solids · Lattice dynamics and thermal properties of solids

Condensed Matter Physics, Ch Elastic waves and the vibrating chain

Problem

A spherical grain of dust, modelled as copper for the purpose of this estimate, has diameter

10\,\mathrm{\mu m}

. Copper has

4

atoms per conventional cubic cell of edge

3.615\,\mathrm{\mathring{A}}

(Chapter 1), giving a number density

n=4/a_{\rm cube}^3

. Estimate ((a)) the number of atoms

N

in the grain and ((b)) the total number of vibrational modes it carries.

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