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  4. A metal exposed to light of wavelength 800 nm and emits photoelectrons with a certain kinetic energy. The maximum kinetic energy of photo-electron doubles when light of wavelength 500 nm is used. The work function of the metal is (Take hc =1230 eV - nm ).

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Q. A metal exposed to light of wavelength $800\, nm$ and emits photoelectrons with a certain kinetic energy. The maximum kinetic energy of photo-electron doubles when light of wavelength $500\, nm$ is used. The work function of the metal is (Take $hc =1230 \,eV - nm )$.

JEE MainJEE Main 2022Dual Nature of Radiation and Matter

Solution:

$ k _1=\frac{1230}{800}-\phi..... $(1)
$ k _2=2 k _1=\frac{1230}{500}-\phi.....$(2)
Eliminating $k _1$ from (1) and (2) we get
$ 0=\frac{1230}{500}-\frac{1230}{400}+\phi$
$ \phi=0.615 \,eV$