SATHEE: dual-nature-of-radiation-and-matter Question 35

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Dual Nature Of Radiation And Matter

dual-nature-of-radiation-and-matter Question 35

Question: Q. 11.8, Page 70]

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Solution:

Ans. Correct option : (c)

Explanation : According to the problem de-Broglie wavelength of electron at time $t = 0$ is $λ_{0} = \frac{h}{m v_{0}}$

Electrostatic force on electron in electric field is

$\vec{F}{e}=-e \vec{E}=-e E{0} \hat{j}$

The acceleration of electron, $\vec{a} = \frac{\vec{F}}{m} = - \frac{e E_{0}}{m} \hat{j}$

It is acting along negative $y$ -axis.

The initial velocity of electron along $x$ -axis, $v_{x_{0}} = v_{0} \hat{i}$ This component of velocity will remain constant as there is no force on electron in this direction. Now considering $y$ -direction. Initial velocity of electron along $y$ -axis, $v_{y 0} = 0$ Velocity of electron after time $t$ along $y$ -axis

$v_{y} = 0 + (- \frac{e E_{0}}{m} \hat{j}) t = - \frac{e E_{0}}{m} t \hat{j}$

Magnitude of velocity of electron after time $t$ is

$\begin{aligned} v & = \sqrt{v_{x}^{2} + v_{y}^{2}} = \sqrt{v_{0}^{2} + {(\frac{- e E_{0}}{m} t)}^{2}} \Rightarrow & = v_{0} \sqrt{1 + \frac{e^{2} E_{0}^{2} t^{2}}{m^{2} v_{0}^{2}}} \end{aligned}$

de-Broglie wavelength, at $t = 0$ is $λ_{0} = \frac{h}{m v_{0}}$

de-Broglie wavelength at $t = t$ is $λ^{'} = \frac{h}{m v}$

Dual Nature Of Radiation And Matter

dual-nature-of-radiation-and-matter Question 35

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Dual Nature Of Radiation And Matter

dual-nature-of-radiation-and-matter Question 35

Very Short Answer Type Questions

Table of Contents

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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