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Dual Nature Of Radiation And Matter

Question

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Light of frequency v falls on material of threshold frequency v_o, Maximum kinetic energy of emitted electron is proportional to

ν - ν_o

ν

$\sqrt{v - v_{o}}$

v_o

Solution

A.

ν - ν_o

When light falls on a metallic surface, ejection of photoelectron results. In this process, conservation
of energy holds.

Thus, from the law of conservation of energy,

Energy imparted by the photon

= Maximum kinetic energy of the emitted electron + work function of the metal

⇒ hv = (KE)_max + $ϕ$

but $ϕ = {hν}_{o}$ being threshold frequency.

∴ ${(KE)}_{\max} = hv - {hv}_{o}$

⇒ (KE)_max ∝ v - v_o

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