A clean molybdenum (100) surface is studied by two separate experiments

PHYSICS · Multi-part · Fermi University Physics · Quantum Mechanics · Condensed Matter, Materials & Soft Matter · Origins of quantum theory

Solid State Physics, Ch The degenerate electron gas, finished

Problem

A clean molybdenum (100) surface is studied by two separate experiments. A photoemission measurement at room temperature finds a photoelectric threshold at wavelength

\lambda_{th}=288\,\mathrm{nm}

, above which no photoelectrons are detected however intense the light. Separately, the same kind of surface, resistively heated to temperatures between

1800\,\mathrm{K}

and

2400\,\mathrm{K}

, is used to record a Richardson plot of

\ln(J/T^2)

against

1/T

, whose slope gives a thermionic work function

\phi_{\rm th}=4.20\,\mathrm{eV}

(already extrapolated to

T=0

, as every Richardson plot is). ((a)) Find the photoelectric work function implied by

\lambda_{th}

, using

hc=1240\,\mathrm{eV\,nm}

. ((b)) State, in one sentence each, what physical energy the photoelectric threshold and the thermionic work function each measure, and explain why they should agree in principle for the same surface. ((c)) The two values differ by about

0.1\,\mathrm{eV}

. Given that the Richardson plot already removes the temperature drift of

\phi

described for tungsten, propose a physical reason for this residual difference, bearing in mind that one surface sat at room temperature and the other was resistively heated to nearly

2400\,\mathrm{K}

for the measurement.

Related theory

Quantum Mechanics

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