Silver has one conduction electron per atom

PHYSICS · Multi-part · Fermi University Physics · Thermal, Statistical & Complex Systems · Statistical mechanics of ideal classical systems · Quantum statistical mechanics and quantum gases

Thermal Physics, Ch The classical ideal gas from the partition function

Problem

Silver has one conduction electron per atom, giving a conduction-electron number density

n = 5.86\times10^{28}\,\mathrm{m^{-3}}

. As a first estimate, treat these electrons at

T = 300\,\mathrm{K}

as a classical gas of free particles of mass

m_e = 9.109\times10^{-31}\,\mathrm{kg}

, ignoring their mutual repulsion and the lattice. Take

h = 6.626\times10^{-34}\,\mathrm{J\,s}

and

k_B = 1.381\times10^{-23}\,\mathrm{J\,K^{-1}}

, and use

\lambda_T = h/\sqrt{2\pi mk_BT}

. ((a)) Estimate the thermal de Broglie wavelength of an electron at

300\,\mathrm{K}

. ((b)) Evaluate the degeneracy parameter

n\lambda_T^3

. ((c)) Feed your result into the Sackur-Tetrode formula

S = Nk_B\!\left[-\ln(n\lambda_T^3) + \tfrac52\right]

and give

S/Nk_B

. What does the sign tell you about applying the classical formulae of this chapter to the electrons in a metal?

Browse the problem library