Book edition 10th Edition

Author(s) David Halliday

Pages 1328 pages

ISBN 9781118230718

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Short Answer

Figure 38-24 shows an electron moving through several regions where uniform electric potentials V have been set up. Rank the three regions according to the de Broglie wavelength of the electron there, greatest first.

The rank is $λ_{2} > λ_{1} > λ_{3}$ .

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Describe the de Broglie wavelength:

The de Broglie wavelength is given by,

$λ = \frac{h}{p}$

Here, h is the Planck's constant, $λ$ is wavelength, and p is the momentum.

The kinetic energy in terms of momentum is given by,

role="math" localid="1663142299185" $K = \frac{p^{2}}{2 m} p = \sqrt{2 m K}$

Here, m is the mass.

Consider an electron, accelerated with a potential difference of V, the kinetic energy is given by,

$K = e V$

The momentum is given by,

$p = \sqrt{2 m e V}$

The expression for wavelength will be as follows:

$λ = \frac{h}{\sqrt{2 m e V}}$

Step 2: Rank the three regions according to the de Broglie wavelength of the electron:

From the above de Broglie wavelength expression, the wavelength is inversely proportional to the $\sqrt{V}$ , which means the wavelength decreases as the potential difference increases and vice-versa.

As given the potential difference,

$V_{1} = - 100 V V_{2} = - 200 V V_{3} = + 100 V$

So, the rank of de Broglie wavelength will be $λ_{2} > λ_{1} > λ_{3}$ .

Therefore, the rank is $λ_{2} > λ_{1} > λ_{3}$ .

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Fundamentals Of Physics

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Short Answer

Figure 38-24 shows an electron moving through several regions where uniform electric potentials V have been set up. Rank the three regions according to the de Broglie wavelength of the electron there, greatest first.

Step by Step Solution

Step 1: Describe the de Broglie wavelength:

Step 2: Rank the three regions according to the de Broglie wavelength of the electron:

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Fundamentals Of Physics

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Short Answer

Figure 38-24 shows an electron moving through several regions where uniform electric potentials V have been set up. Rank the three regions according to the de Broglie wavelength of the electron there, greatest first.

Step by Step Solution

Step 1: Describe the de Broglie wavelength:

Step 2: Rank the three regions according to the de Broglie wavelength of the electron:

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