Book edition 10th Edition

Author(s) David Halliday

Pages 1328 pages

ISBN 9781118230718

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Short Answer

Show that Eq. 41-9 can be written as $E_{F} = A n^{2 / 3}$ where the constant A has the value role="math" localid="1661507403881" $3.65 \times 10^{- 19} m^{2} eV$ .

It is shown that the Energy of the Fermi level is $E_{F} = A n^{2 / 3}$ , where the value of A is $3.65 \times 10^{- 19} m^{2} eV$ .

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: The given data

The equation of Fermi energy according to Eq. 41-9 is $E_{F} = {[\frac{3}{16 \sqrt{2} π}]}^{2 / 3} \frac{h^{2}}{m} n^{2 / 3}$ .

where n is the number density of free electrons, m is the electron’s mass and h is Planck’s constant.

Step 2: Understanding the concept of Fermi energy

The highest energy level occupied by the electrons in the valence band at a temperature equal to zero Kelvin is known as the Fermi level and the energy of electrons in that level is known as Fermi energy.

Step 3: Calculation of the Fermi energy and the constant value A

From the given equation of Fermi energy, we can see that the energy is directly related to the number of conduction electrons having all other terms as constants. Thus, the formula for Femi energy can also be written as-

$E_{F} = A n^{2 / 3}$

Where

$A = {[\frac{3}{16 \sqrt{2} π}]}^{2 / 3} \frac{h^{2}}{m} = {[\frac{3}{16 \sqrt{2} π}]}^{2 / 3} \frac{{(6.63 \times 10^{- 34} J \cdot s)}^{2}}{9.1 \times 10^{- 31} kg} = 5.842 \times 10^{- 38} J^{2} . s^{2} / kg$

Since $1 J = 1 kg \cdot m^{2} / s^{2}$ the units of A can also be written as-

$A = 5.84 \times 10^{- 38} m^{2} . J$

If we divide the term by $1.6 \times 10^{- 19} J / eV$ , we have

$A = \frac{5.84 \times 10^{- 38} m^{2} . J}{1.6 \times 10^{- 19} J / eV} = 3.65 \times 10^{- 19} m^{2} eV$

Hence, the value of the Fermi energy is $E_{F} = A n^{2 / 3}$ , where the value of A is $3.65 \times 10^{- 19} m^{2} eV$ .

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Fundamentals Of Physics

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Short Answer

Show that Eq. 41-9 can be written as $E_{F} = A n^{2 / 3}$ where the constant A has the value role="math" localid="1661507403881" $3.65 \times 10^{- 19} m^{2} eV$ .

Step by Step Solution

Step 1: The given data

Step 2: Understanding the concept of Fermi energy

Step 3: Calculation of the Fermi energy and the constant value A

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Fundamentals Of Physics

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Short Answer

Show that Eq. 41-9 can be written as EF=An2/3where the constant A has the value role="math" localid="1661507403881" 3.65×10-19 m2eV.

Step by Step Solution

Step 1: The given data

Step 2: Understanding the concept of Fermi energy

Step 3: Calculation of the Fermi energy and the constant value A

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Show that Eq. 41-9 can be written as $E_{F} = A n^{2 / 3}$ where the constant A has the value role="math" localid="1661507403881" $3.65 \times 10^{- 19} m^{2} eV$ .