What is the wavelength of a photon incident on the silver surface if the maximum speed of photoelectrons is 250 km / s? the work function for silver is 4.7 eV.
V = 250 km / s = 250,000 m / s.
m = 9.1 * 10 ^ -31 kg.
h = 6.6 * 10 ^ -34 J * s.
c = 3 * 10 ^ 8 m / s.
Av = 4.7 eV = 7.52 * 10 ^ -19 J.
Let us write down the condition of the photoelectric effect: h * c / λ = Av + Ek, where h * c / λ is the energy of the incident photons, Ek is the kinetic energy of electrons that fly out of the metal surface.
The kinetic energy of electrons Ek is determined by the formula: Ek = m * V ^ 2/2, where m is the mass of an electron, V is the velocity of the emitted electrons.
h * c / λ = Ab + m * V ^ 2/2.
λ = h * c / (Ab + m * V ^ 2/2).
λ = 6.6 * 10 ^ -34 J * s * 3 * 10 ^ 8 m / s / (7.52 * 10 ^ -19 J + 9.1 * 10 ^ -31 kg * (250,000 m / s) ^ 2/2) = 0.25 * 10 ^ -6 m.
Answer: the incident light has a wavelength λ = 0.25 * 10 ^ -6 m.
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