A clean molybdenum filament is heated in vacuum and the saturated thermionic current…

PHYSICS · Multi-part · Fermi University Physics · Scientific Practice & Experimental Methods · Condensed Matter, Materials & Soft Matter · Data analysis and model fitting in the laboratory

Solid State Physics, Ch The degenerate electron gas, finished

Problem

A clean molybdenum filament is heated in vacuum and the saturated thermionic current density JJ is measured at two temperatures: J=3.50×10−3 A cm−2J=3.50\times10^{-3}\,\mathrm{A\,cm^{-2}} at T=2000 KT=2000\,\mathrm{K} and J=0.806 A cm−2J=0.806\,\mathrm{A\,cm^{-2}} at T=2500 KT=2500\,\mathrm{K}. The Richardson equation is J=A0T2e−ϕ/kBTJ = A_0 T^2 e^{-\phi/k_BT}, where ϕ\phi is the work function and A0A_0 the (possibly reduced) Richardson constant, with universal value 120 A cm−2K−2120\,\mathrm{A\,cm^{-2}K^{-2}}. ((a)) Convert both (T,J)(T,J) pairs into the two coordinates (1/T, ln⁡(J/T2))\left(1/T,\ \ln(J/T^2)\right) used for a Richardson plot. ((b)) Use these two points to find the work function ϕ\phi, in eV. ((c)) Find the effective Richardson constant A0A_0 from the intercept, and express it as a fraction of the universal value 120 A cm−2K−2120\,\mathrm{A\,cm^{-2}K^{-2}}.

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