The answer is supposed to be 8.56x10 -9 A, but I can\'t figure out where they we

Question

The answer is supposed to be 8.56x10-9 A, but I can't figure out where they went wrong in this method, and nobody has corrected it even though it has 7 downvotes, so I figured I'd ask seperately. I've seen a few other explanations that use a different method, but they use a formula that I can't find in my textbook, so I'm not sure that's the "correct" method that my professor is expecting...

Problem A 2 0 mw green laser (A-532 nm) shines on a cesium photocathode (-1.95 eV) Assume an etmiciency ot 105 tor producing photoelectrons (that is, one photoelectron produced tor every 103 incident photons) and determine the photoelectric current. Step-by-step solution Step 1 of 5 The Einstein's photo-clectric equation, Here. h s Plank's constant f is frequency of photon, s work tunction of emitter of electron andis maximum velocity of electron From the law of conservation of energy, the kinetic energy of the photo electrons, m is mass Here, is applied voltage Comment Step 2 of 5 The Einstein's photo-clectric equation, Here. , ts Plank's constant f is frequency of photon, s work function of emitter of electron ands maximum velocity of electron From the law of conservation of energy, the kinetic energy of the photo electrons, m is mass vina,-0% (2) Here, is applied voltage. From equation (1) and equation (2), Rearrange above expression for V Frequency of the electron is given by Here, cs velocity of light and is wavelength of the light. From equaton (3) arnd equation (4). Substitute 6.67x 10-34 m2, kg/s for h 3x10" m/s tor cand 530 nm for 3x10 m/s 6.67x 10 m2 (1.95 ev) .6x10J 532 nm 1.6×10-19 C 6.67x10 34 m12-kg/s(5.63x10 14)-3. 12x10 19 J 1.6x10-19 C 3.76x1019 J-3.12x10-19 J 1.6x10-19 C = 0.4 V

Explanation / Answer

given

laser power P = 2 mW = 2*10^-3 W
lambda = 532 nm = 532*10^-9 m
phi = 1.95 eV
n = 10^-5

so in one second
energy = 2*10^-3 J
number of photons N = 2*10^-3*lambda/hc = 5.34136*10^15 photons

now, energy of each photon = hc/lambda = 3.744*10^-19 J = 2.340225 eV
this is more than the work function phi
hence

photocurrent = charge on nN electrons
i = N*10^-5*1.6*10^(-19) = 8.546176*10^-9 A

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