Spring 2010 Solutions - FSU Physics Department
Spring 2010 Solutions - FSU Physics Department Spring 2010 Solutions - FSU Physics Department
Problem 10Light of wavelength 300 nm strikes a metal plate, producing photoelectrons that movewith speed of 0.002c.(a) What is the work function of the metal?(b) What is the critical wavelength for this metal, so that photoelectrons are produced?(c) What is the significance of the critical wavelength?SolutionLight of wavelength 300 nm strikes a metal plate, producing photoelectrons thatmove with speed of 0.002c.In the photoelectric effect the incoming photons remove electrons from the target.There is a minimum energy required to remove an electron from the interior of asolid to a position just outside. This minimum energy is called the work functionΦ. The relation between the energy of photon Eγ , the energy of electron Ee, andthe work function Φ is given byE = Ee + Φ (1)Note that energy of electron Ee is equal to the kinetic energy of electron, sincewhen electron is outside the solid it is not affected by any potential. In other wordselectron will be considered as a free particle.(a) What is the work function of the metal?Use Eq.1, since the speed of the electron is much less than speed of the lightwe do not need to use the special relativity formula for the kinetic energy.Ee = (1/2)mv 2 (2)= (1/2) (511keV/c 2 ) (0.002c) 2 =1.022eV (3)Eγ = hυ = hc/λ (4)= (1420 eV nm/300 nm) = 4.13 eV (5)Φ = Eγ – Ee (6)= 3.111 eV (7)(b) What is the critical wavelength for this metal, so that photoelectronsare produced ?The critical wavelength is defined as the wavelength for photons which removeelectrons from interior of a solid to a position outside the solid. Inthis case the kinetic energy of electrons outside the solid is equal zero Ee = 0.Using the Eq.1 and the results from part (a) we obtain
Eγ = Φ (8)hc/ λcritical = Φλcritical = hc/Φ (9)λcritical =1420 eV/3.111 eVλcritical = 398.6 eV (10)(c) What is the significance of the critical wavelength?Photons with a lower wavelength than the critical wavelength cannot produce photoelectrons.This led Einstein to the postulation of quantized energy for the electromagneticfields.
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Eγ = Φ (8)hc/ λcritical = Φλcritical = hc/Φ (9)λcritical =1420 eV/3.111 eVλcritical = 398.6 eV (10)(c) What is the significance of the critical wavelength?Photons with a lower wavelength than the critical wavelength cannot produce photoelectrons.This led Einstein to the postulation of quantized energy for the electromagneticfields.
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