Comparing photon energy with a supplied work function
An idealized photoelectric experiment uses a clean hypothetical emitting surface with work function 2.30 eV. The surface name is deliberately unspecified: the work function is a supplied model parameter. Two narrow-band light sources have wavelengths 400 nm and 600 nm. For this exercise use hc = 1240 eV nm and the ordinary single-photon photoelectric model. Assume the apparatus measures the stopping potential without contact-potential offsets, that unwanted background currents are negligible and that the illumination is weak enough for multiphoton processes to be neglected. A student expects the brighter 600 nm beam eventually to produce electrons with the same maximum energy as the 400 nm beam. The group must separate photon energy from photon arrival rate and state what would change if the 400 nm intensity doubled.
1. Find whether each source causes emission and calculate any maximum kinetic energy and stopping potential.
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At 400 nm, photon energy is 1240/400 = 3.10 eV. Maximum emitted-electron kinetic energy is 3.10 - 2.30 = 0.80 eV, corresponding to a stopping-potential magnitude of 0.80 V under the supplied measurement assumptions. At 600 nm, photon energy is 2.067 eV, below 2.30 eV, so the specified single-photon model predicts no emission. A negative calculated kinetic energy means emission is forbidden in this model, not that an emitted electron has negative kinetic energy.
2. Explain the effect of doubling intensity at 400 nm and identify the threshold wavelength.
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At fixed wavelength every photon retains the same energy. Doubling incident photon flux can double the emitted-electron rate in the ideal proportional-response regime, but does not change the maximum kinetic energy or stopping potential. Threshold wavelength is hc/work function = 1240/2.30 = 539.1 nm. Wavelengths longer than this lack sufficient single-photon energy; increasing their ordinary intensity does not change that threshold conclusion.