Lithium metal has mass density

PHYSICS · Multi-part · Fermi University Physics · Condensed Matter, Materials & Soft Matter · Free electrons, energy bands and electronic structure · Free electrons, energy bands and electronic structure

Solid State Physics, Ch The degenerate electron gas, finished

Problem

Lithium metal has mass density ρm=0.534 g cm−3\rho_m=0.534\,\mathrm{g\,cm^{-3}}, molar mass M=6.94 g mol−1M=6.94\,\mathrm{g\,mol^{-1}}, and contributes Z=1Z=1 conduction electron per atom. Its measured electronic heat capacity coefficient (tabulated, low-temperature specific-heat measurement) is γexpt=1.63 mJ mol−1K−2\gamma_{\rm expt}=1.63\,\mathrm{mJ\,mol^{-1}K^{-2}}. ((a)) Find the conduction-electron number density nn. ((b)) Treating lithium as a free-electron gas, find EFE_F and the free-electron heat-capacity coefficient γfree\gamma_{\rm free}, expressed in mJ mol−1K−2\mathrm{mJ\,mol^{-1}K^{-2}}. ((c)) Compute the thermal mass mth/me=γexpt/γfreem_{\rm th}/m_e=\gamma_{\rm expt}/\gamma_{\rm free}. ((d)) Name the two mechanisms that could between them produce this thermal mass, and say explicitly why the heat-capacity data alone cannot tell how much each contributes.

Browse the problem library