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A metal plate carrying a uniform surface charge density of +2*epsilon₀ C/m² (in SI units) is illuminated with photons of wavelength 620 nm. The work function of the metal is 1.5 eV. Assuming photoelectrons are emitted perpendicular to the plate, what is the maximum distance from the plate that an ejected photoelectron can travel before being pulled back by the electric field?

1. No photoelectrons will be emitted
2. Photoelectrons will not turn back at all
3. 1/4 m
4. 1/2 m

Correct answer: 1/2 m

Solution

The photon energy is approximately 2 eV and work function is 1.5 eV, so KE_max = 0.5 eV = 8*10⁻²⁰ J. The electric field from the plate is E = sigma/(2*epsilon₀) = 1 V/m, so the electron is decelerated at a = eE/mₑ. Using KE = e*E*d, d = 0.5 eV / (e * 1 V/m) = 0.5 m = 1/2 m.

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