A beam of light has three wavelengths $4000 A^{°}, 5000 A^{°}$ and $6000 A^{°}$ with a total intensity of $3 \times 10^{- 3} \frac{W}{m^{2}}$ equally distributed amongst the three wavelengths. The beam fall normally on an area $2 c m^{2}$ of clean metallic surface of work function 2.4 eV. If quantum yield of photoemission is 1%, then the saturation photocurrent is $x \times 10^{- 9} A$ . Find x (Take hc=12400 eV. $A^{°}$ )

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answer is 1.4.

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Detailed Solution

$λ_{t h} = \frac{12400}{2.4} = 5167 A^{0} ∴ 4000 A^{°} a n d 5000 A^{°} o n l y a r e e n e r g e t i c a l l y c a p a b l e . ∴ i = (\frac{I_{1} A_{1} λ_{1}}{h c} + \frac{I_{2} A_{2} λ_{2}}{h c}) e η = 1 \times 10^{- 3} \times 2 \times 10^{- 4} \frac{(λ_{1} + λ_{2})}{h c} \times e \times 10^{- 2} = 2 \times 10^{- 7} \times \frac{9000}{12400} \times 10^{- 2} = 1.45 \times 10^{- 9} A$