A student predicts the density of silicon (

PHYSICS · Subjective · Fermi University Physics · Condensed Matter, Materials & Soft Matter · Crystal structure, bonding and diffraction · Crystal structure, bonding and diffraction

Condensed Matter Physics, Ch What holds a solid together, and where its atoms sit

Problem

A student predicts the density of silicon (a=5.431 A˚a=5.431\,\mathrm{\mathring{A}}, molar mass 28.09 g mol−128.09\,\mathrm{g\,mol^{-1}}) this way: "Silicon is face-centred cubic, so Zc=4Z_c=4, and ρ=4×28.09/(NAa3)=1.165 g cm−3\rho=4\times28.09/(N_Aa^3)=1.165\,\mathrm{g\,cm^{-3}}." This is roughly half the measured density, 2.329 g cm−32.329\,\mathrm{g\,cm^{-3}}. Find the error, and correct the calculation.

Browse the problem library