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  4. Light of two different frequencies whose photons have energies 1 eV and 2.5 eV respectively, successively illuminate a metallic surface whose work function is 0.5 eV. Ratio of maximum speeds of emitted electrons will be

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Q. Light of two different frequencies whose photons have energies $1\, eV$ and $2.5\, eV$ respectively, successively illuminate a metallic surface whose work function is $0.5\, eV$.
Ratio of maximum speeds of emitted electrons will be

AIIMSAIIMS 2017Dual Nature of Radiation and Matter

Solution:

$v _{\max } =\sqrt{\frac{2}{ m } K \cdot E _{\max }} $
$v _{\max } =\sqrt{\frac{2}{ m }\left( E _{ Ph }- W \right)} $
$\frac{ v _{1}}{ v _{2}} =\sqrt{\frac{ E _{ Ph _{1}}- W }{ E _{ Ph _{2}}- W }} $
$=\sqrt{\frac{1-0.5}{2.5-0.5}}$
$\frac{ v _{1}}{ v _{2}} =\frac{1}{2}$