A small potassium foil is placed (perpendicular$$ to the direction of incidence of $$light) a distance r $$(=$$ $$0.5$$ $$m)$$ from a point light source whose output power $$P0$$ is $$1.0$$ W. Assuming wave nature of light how long (in$$ $$s) would it take for the foil to soak up enough energy $$(=$$ $$1.8$$ $$eV)$$ from the beam to eject an electron? Assume that the ejected photoelectron collected its energy from a circular area of the foil whose radius equals the radius of a potassium atom (1.3$$ x $$10-10$$ $$m).

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Infinity Learn · Accepted Answer

If the source radiates uniformly in all directions, the intensity I of the light at a distance r is given $$byI=P04$$$$π$$$$r2=1.0W4$$π$$(0.5m)2=0.32W/m2The$$ target area A is $$n(1.3$$ x $$10-10$$ $$m)2$$ or $$5.3$$ x $$10-20m2$$, so that the rate at which energy falls on the target is given $$byP=IA=0.32W/m25.3$$×$$10$$−$$20m2=1.7$$×$$10$$−$$20J/sIf$$ all this incoming energy is absorbed, the time required to accumulate energy for the electron to escape $$ist=1.8eV1.7$$×$$10$$−$$20J/s1.6$$×$$10$$−$$191eV=17s$$

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