Dual Nature of Radiation and Matter - Result Question 9

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======= ####9. The wavelength $λ_{e}$ of an electron and $λ_{p}$ of a photon are of same energy $E$ are related by [2013]

c3eec34ec6b1fad69db54a20ad4b2dca40c2aa54 (a) $λ_{p} \propto λ_{e}$

(b) $λ_{p} \propto \sqrt{λ_{e}}$

(d) $λ_{p} \propto λ_{e}^{2}$

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Answer:

Correct Answer: 9. (d)

Solution:

(d) $A s P = \frac{E}{c}$

$λ_{p} = \frac{h c}{E}$

$λ_{e} = \frac{h}{\sqrt{2 m E}} \Rightarrow λ_{e}^{2} = \frac{h^{2}}{2 m E}$

From equations (i) and (ii)

$λ_{p} \propto λ_{e}^{2}$

de-Broglie wavelength, $λ = \frac{h}{p}$

Here, $h =$ plank’s constant

$p =$ momentum

Momentum, $p = \sqrt{2 m k}$

$∴ λ = \frac{h}{\sqrt{2 m E}}$ (Here, $E =$ kinetic energy)

$∴ E = \frac{h^{2}}{2 m λ^{2}} \Rightarrow λ^{2} = \frac{h^{2}}{2 m E}$

Dual Nature of Radiation and Matter - Result Question 9

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Dual Nature of Radiation and Matter - Result Question 9

9. The wavelength λe of an electron and λp of a photon are of same energy E are related by [2013]

«««< HEAD

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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9. The wavelength $λ_{e}$ of an electron and $λ_{p}$ of a photon are of same energy $E$ are related by [2013]