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If p is the momentum of the fastest electron ejected from a me

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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;

\frac{4}{9} λ

\frac{3}{4} λ

\frac{2}{3} λ

\frac{1}{2} λ

Views: 5,373 students

Updated on: Aug 21, 2023

Book:

Arihant Chemistry JEE Main Chapterwise Solutions (2019-2002) (Arihant)

Exam:

JEE Mains 2019

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Lucas Discussed

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;

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Text solutionVerified

The expression of kinetic energy of photo electrons,

KE = \frac{1}{2} m v^{2} = E - E_{0}

When,

KE >> E_{0}

, the equation becomes,

KE = \frac{1}{2} m v^{2} = E

\Rightarrow \frac{1}{2} m v^{2} = \frac{h c}{λ} \Rightarrow \frac{p ^{2}}{2 m ^{2}} = \frac{h c}{λ}

\Rightarrow λ = h c \times 2 m^{2} \times \frac{1}{p ^{2}}

\Rightarrow λ \propto \frac{1}{p ^{2}}

E = \frac{h c}{λ} =

energy of incident light.

E_{0} =

threshold energy or work functions,

\frac{1}{2} m v^{2} = \frac{1}{2} \times \frac{( m v ) ^{2}}{m ^{2}} = \frac{1}{2} \times \frac{p ^{2}}{m ^{2}}

∵ p =

momentum

= m v

As per the given condition,

\Rightarrow \frac{λ _{2}}{λ _{1}} = (\frac{p _{1}}{p _{2}})^{2}

\Rightarrow \frac{λ _{2}}{λ} = (\frac{p}{1.5 \times p})^{2} = (\frac{2}{3})^{2} = \frac{4}{9}

\Rightarrow λ_{2} = \frac{4}{9} λ

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Question Text	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;
Updated On	Aug 21, 2023
Topic	Structure of Atom
Subject	Chemistry
Class	Class 11
Answer Type	Text solution:1 Video solution: 13
Upvotes	1448
Avg. Video Duration	7 min

Text solutionVerified

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