Chemistry - Atomic Structure Question with Solution | TestHub

ChemistryAtomic StructurePhotoelectric EffectMedium2 minPYQ_2019

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If $p$ is the momentum of the fastest electron ejected from a metal surface after the irradiation of light having wavelength $λ,$ then for $1.5 p$ momentum of the photoelectron, the wavelength of the light should be:

(Assume kinetic energy of ejected photoelectron to be very high in comparison to work function)

Options:

Answer:

Solution:

$h ν - ϕ = K E$

${(\frac{h c}{λ})}_{i n c i d e n t} = K E + ϕ$

Given $(ϕ < < K E)$

${(\frac{h c}{λ})}_{i n c i d e n t} \approx K E$

${(\frac{h c}{λ})}_{i n c i d e n t} = \frac{p^{2}}{2 m}$ ......(i)

$(\frac{h c}{λ'}) = \frac{{(1.5 p)}^{2}}{2 m}$ …….(ii)

Divide (i) and (ii)

$\frac{λ^{'}}{λ} = \frac{p^{2}}{2.25 p^{2}}$

$λ^{'} = \frac{λ \times 100}{2.25} = \frac{4}{9}$

$λ^{'} = \frac{4}{9} λ$

Stream:JEESubject:ChemistryTopic:Atomic StructureSubtopic:Photoelectric Effect

⏱ 2mℹ️ Source: PYQ_2019

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