Dual Nature of Matter

JEE Main level, single correct, medium

181 of 200

Question 181 of 200

A photoelectric surface is illuminated successively by monochromatic light of wavelengths λandλ2.\lambda and\dfrac{\lambda }{2}. If the maximum kinetic energy of the emitted photoelectrons in the second case is 3 times that in the first case, the work function of the surface is :

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Answer: (A) hc2λ\dfrac{hc}{2\lambda }

K.Eλ=hcλ−ϕK.{E}_{\lambda }=\dfrac{hc}{\lambda }-\phi

K.Eλ2=hcλ2−ϕK.{E}_{\dfrac{\lambda }{2}}=\dfrac{hc}{\dfrac{\lambda }{2}}-\phi

K.Eλ2=3(K.Eλ)K.{E}_{\dfrac{\lambda }{2}}=3\left(K.{E}_{\lambda }\right)

⇒ϕ=hc2λ\Rightarrow \phi =\dfrac{hc}{2\lambda }

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