Book edition 10th Edition

Author(s) David Halliday

Pages 1328 pages

ISBN 9781118230718

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Short Answer

X rays of wavelength 0.0100 nm are directed in the positive direction of an axis onto a target containing loosely bound electrons. For Compton scattering from one of those electrons, at an angle of $180 °$ , what are (a) the Compton shift, (b) the corresponding change in photon energy, (c) the kinetic energy of the recoiling electron, and (d) the angle between the positive direction of the axis and the electron’s direction of motion?

(a) The Compton shift is $+ 4.86 pm$ .

(b) The change in photon energy is $- 40.6 keV$ .

(d) The angle between positive direction of +x axis and the electron direction of motion is zero.

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Evaluate the Compton shift

(a)

Use the Compton shift formula is:

$Δ λ = \frac{h}{m_{e} c} (1 - \cos ϕ) = (2.43 pm) (1 - \cos 180 °) = + 4.86 pm$

Hence, the Compton shift is +4.86 pm.

Step 2: The corresponding change in photon energy

(b)

Let the value of $h c = 1240 eV \cdot nm$ .

Use the above value to find the change in photon energy is;

$Δ E = \frac{h c}{λ'} - \frac{h c}{λ} = 1240 (\frac{1}{0.01 nm + 4.86 nm} - \frac{1}{0.01 nm}) = - 40.6 keV$

Hence, the change in photon energy is $- 40.6 keV$ .

Step 3: The kinetic energy of recoiling electron

(c)

Use the conservation of energy, that the energy neither be created nor be destroyed it only be transformed from one energy to another.

From the conservation of energy,

$Δ K = - Δ E = 40.6 keV$

Hence, the kinetic energy of recoiling electron is 40.6 keV.

Step 3: The angle between positive direction of x axis and the electron direction of motion

(d)

The electron will move straight ahead after the collision, since it has acquired some of the forward linear momentum from the photon. Thus, the angle between +x and the direction of the electron’s motion is zero.

Hence, the angle between positive direction of +x axis and the electron direction of motion is zero.

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Fundamentals Of Physics

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Short Answer

Step by Step Solution

Step 1: Evaluate the Compton shift

Step 2: The corresponding change in photon energy

Step 3: The kinetic energy of recoiling electron

Step 3: The angle between positive direction of x axis and the electron direction of motion

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Step by Step Solution

Step 1: Evaluate the Compton shift

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Step 3: The angle between positive direction of x axis and the electron direction of motion

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