Dual Nature of Matter

JEE Main level, numerical answer, medium

160 of 200

Question 160 of 200

Two stream of photons, possessing energies equal to twice and ten times the work function of metal are incident on the metal surface successively. The value of ratio of maximum velocities of the photoelectrons emitted in the two respective cases is x:3x:3 The value of xx is

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Answer: 1

KEmax⁡=hν−ϕK{E}_{\max }=h\nu -\phi
12mv2=hν−ϕ\dfrac{1}{2}m{v}^{2}=h\nu -\phi
v=2(hν−ϕ)mv=\sqrt{\dfrac{2\left(h\nu -\phi \right)}{m}}
Given hν1=2ϕh{\nu }_{1}=2\phi
hν2=10ϕh{\nu }_{2}=10\phi
∴v1v2=hν1−ϕhν2−ϕ∴\dfrac{{v}_{1}}{{v}_{2}}=\sqrt{\dfrac{h{\nu }_{1}-\phi }{h{\nu }_{2}-\phi }}
v1v2=2ϕ−ϕ10ϕ−ϕ=13\dfrac{{v}_{1}}{{v}_{2}}=\sqrt{\dfrac{2\phi -\phi }{10\phi -\phi }}=\dfrac{1}{3}

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