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A metal plate is illuminated by light of wavelength lambda. Electrons are ejected from the plate surface. A uniform retarding electric field E is applied, and no electron can travel more than a distance d from the plate. If e is the electronic charge, h is Planck's constant, and c is the speed of light, find the threshold wavelength lambda0 of the metal.
- lambda0 = (1/lambda - hc/(e*E*d))^(-1)
- lambda0 = (1/lambda - e*E*d/(hc))^(-1)
- lambda0 = lambda - hc/(e*E*d)
- lambda0 = lambda - e*E*d/(hc)
Correct answer: lambda0 = (1/lambda - e*E*d/(hc))^(-1)
Solution
By Einstein's photoelectric equation: KE_max = hc/lambda - hc/lambda0 (where hc/lambda0 is the work function). The retarding field E stops the fastest electron within distance d, so KE_max = e*E*d. Therefore: e*E*d = hc/lambda - hc/lambda0. Rearranging: hc/lambda0 = hc/lambda - e*E*d. Dividing by hc: 1/lambda0 = 1/lambda - e*E*d/(hc). So lambda0 = 1/(1/lambda - e*E*d/(hc)) = (1/lambda - e*E*d/(hc))^(-1).
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