Book edition 10th Edition

Author(s) David Halliday

Pages 1328 pages

ISBN 9781118230718

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Short Answer

Calculate the density of states $N (E)$ for metal at energy $E = 8.0 e V$ and show that your result is consistent with the curve of Fig. 41-6.

The density of states $N (E)$ for metal is $1.9 \times 10^{28} m^{- 3} . {(eV)}^{- 1}$ and it is consistent with the curve of figure 41-6.

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: The given data

Energy of the metal, $E = 8 eV$

Step 2: the concept of density of states

The number of states per unit energy range per unit volume $(N (E))$ , present in a sample of the material at a particular energy $(E)$ , is known as density of states. The formula for density of states is given as-

$N (E) = \frac{8 \sqrt{2} {πm}^{3 / 2}}{h^{3}} E^{1 / 2} . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (1) where h = 6.63 \times 10^{- 34} J . s and m = 9.1 \times 10^{- 31} kg$

Step 3: Calculation of the density of states of a metal

We can write equation (1) as follows:

$N (E) = C E^{1 / 2}$

In the above equation, the value of C is -

$C = \frac{8 \sqrt{2} {πm}^{3 / 2}}{h^{3}} = \frac{8 \sqrt{2} π {(9.1 \times 10^{- 31} kg)}^{3 / 2}}{(6.63 \times 10^{- 34} J . s)} = 1.062 \times 10^{56} {kg}^{3 / 2} / J^{3} . s^{3} = 6.81 \times 10^{27} m^{- 3} . {(eV)}^{- 2 / 3}$

Using the given data in equation (1), the density of states for the metal with energy $E = 8 e V$ can be calculated as follows:

$N (E) = [6.81 \times 10^{27} m^{- 3} . {(eV)}^{- 2 / 3}] {(8 eV)}^{1 / 2} = 1.9 \times 10^{28} m^{- 3} . {(eV)}^{- 1}$

This value of density of state is consistent with the given figure 41-6.

Hence, the value of the density of states is $1.9 \times 10^{28} m^{- 3} . {(eV)}^{- 1}$ .

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Fundamentals Of Physics

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Short Answer

Calculate the density of states $N (E)$ for metal at energy $E = 8.0 e V$ and show that your result is consistent with the curve of Fig. 41-6.

Step by Step Solution

Step 1: The given data

Step 2: the concept of density of states

Step 3: Calculation of the density of states of a metal

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Fundamentals Of Physics

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Short Answer

Calculate the density of states N(E) for metal at energy E=8.0eVand show that your result is consistent with the curve of Fig. 41-6.

Step by Step Solution

Step 1: The given data

Step 2: the concept of density of states

Step 3: Calculation of the density of states of a metal

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Calculate the density of states $N (E)$ for metal at energy $E = 8.0 e V$ and show that your result is consistent with the curve of Fig. 41-6.