5) Photoelectric effect
A beam of ultraviolet light of intensity 1.6×10-12watts (=107eV/s) is suddenly turned on and falls on a metal surface, ejecting electrons through the photoelectric effect. The beam has a cross sectional area of 1 cm2, and the wavelength corresponds to a photon energy of 10 eV. The work function of the metal is 5 eV. How soon might one expect photoelectric emission to occur?
a) Compute, with a classical estimation, the time needed for the work-function energy (5 eV) to be accumulated over the area of one atom (radius ≈ 1Angstrom), assuming the energy of the light beam to be uniformly distributed over its cross section.
b) Actually, as Lord Rayleigh showed [Phil. Mag. 32, 188 (1916)] the estimate from (a) is too pessimistic. An atom can present an effective area of about λ2 to light of wavelength λ corresponding to its resonant frequency. Calculate a classical delay time on this basis.
c) On the quantum picture of this process, it is possible for photoelectric emission to begin immediately – as soon as the first photoelectron strikes the emitting surface. But to obtain a time that may be compared to the classical estimates, calculate the average time interval between the arrival of consecutive 10eV photons. This would also be the average time delay between switching on the beam and getting the first photoelectron.
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