In a Photoelectric effect setup, a point source of light of power \( 3.2 \times 10^{-3} \mathrm{...

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In a Photoelectric effect setup, a point source of light of power \( 3.2 \times 10^{-3} \mathrm{~W} \) emits mono energetic photons of energy \( 5.0 \mathrm{eV} \). The source is located at a distance of \( 0.8 \mathrm{~m} \) from the centre of a stationary metallic sphere of work function \( 3.0 \mathrm{eV} \) \( \& \) of radius \( 8.0 \times 10^{-3} \mathrm{~m} \). The efficiency of photo electrons emission is one for every \( 10^{6} \) incident photons. Assume that the sphere is isolated and initially neutral, and that photo electrons are instantly swept away after emission.
(a) Calculate the number of photo electrons emitted per second
(b) Find the ratio of the wavelength of incident light to the de-Broglie wave length of the fastest photo electrons emitted
(c) Evaluate the time \( t \)
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