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A metal plate is placed 5 metre from a monochromatic light source whose power output is $10^{- 3} W$ , Consider that a given created photoelectrons may collect its energy from a circular area of the plate as large as ten atomic diameters $(10^{- 9} m)$ in radius. The energy required to remove an electron through the metal surface is about $5 e V$ . Assuming light to be a wave, how long, in hour, would it take for such a 'target' to soak up this much energy from such a light source.

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Detailed Solution

The target area is $S_{1} = π {(10^{- 9})}^{2} = π \times 10^{- 18} m^{2}$ .

The area of a 5 metre sphere centred on the light source is, $S_{2} = 4 π (5)^{2} = 100 π m^{2}$ .

Thus, if the light source radiates uniformly in all directions the rate P at which energy falls on the target is given by,

$P = (10^{- 3} W) (\frac{S_{1}}{S_{2}}) = (10^{- 3}) (\frac{π \times 10^{- 18}}{100 \times π}) W$
$\Rightarrow P = 10^{- 23} W$

Assuming that all power is absorbed, the required time is,

$t = \frac{E}{P} = \frac{(5) \times (1.6 \times 10^{- 19})}{(10^{- 23})} = 8 \times 10^{4} s = \frac{80000}{3600} hr \approx 22 hr$

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