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HW Key _4 S problems part a

HW Key _4 S problems part a - S11 Alarm systems employ the...

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S11. Alarm systems employ the photoelectric effect. A beam of light strikes a piece of metal in a photocell, ejecting electrons continuously and causing a small electric current to flow. When someone steps into the light beam, the current is interrupted and the alarm is triggered. a. What is the maximum wavelength of light that can be used in such an alarm system if the photocell metal is sodium, with a work function of 4.41 x 10 -19 J? The maximum wavelength of light is the wavelength that supplies photons with just enough energy to overcome the work function of the surface. The work function of the molecule, Φ , is related to the minimum frequency according to the expression Φ = h ν 0 Recognizing that wavelength and frequency are related according to c = λν . Substituting this into the above expression and solving for wavelength gives Φ = hc λ λ = hc Φ = (6.626 × 10 34 Js)(2.9979 × 10 8 m) 4.41 × 10 19 J = 4.50 × 10 7 m = 450 nm b. What is the minimum frequency?
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