Dual Nature of Matter

JEE Main level, single correct, medium

166 of 200

Question 166 of 200

When the wavelength of radiation falling on a metal is changed from 500nmto200nm500nmto200nm, the maximum kinetic energy of the photoelectrons becomes three times larger. The work function of the metal is close to:

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Answer: (D) 0.61eV0.61eV

KEmax=hcλ−ϕ=hc500−ϕ{KE}_{max}=\dfrac{hc}{\lambda }-\phi =\dfrac{hc}{500}-\phi .....(i)
Now,
3KEmax⁡=hc200−ϕ3{KE}_{\max }=\dfrac{hc}{200}-\phi
.....(ii)
From equation (i) and (ii)
(ii)(i)=31=hc200−ϕhc500−ϕ\dfrac{\left(ii\right)}{\left(i\right)}=\dfrac{3}{1}=\dfrac{\dfrac{hc}{200}-\phi }{\dfrac{hc}{500}-\phi }
Put the value of hc=1237.5hc=1237.5 and solving ϕ=0.61eV\phi =0.61eV

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