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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.

The density of states NE for metal is 1.9×1028m-3.eV-1 and it is consistent with the curve of figure 41-6.

See the step by step solution

Step by Step Solution

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 (NE), 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-

NE=82πm3/2h3E1/2.............................1where h=6.63×10-34 J.s and m=9.1×10-31 kg

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

We can write equation (1) as follows:


In the above equation, the value of C is -

C=82πm3/2h3 =82π9.1×10-31 kg3/26.63×10-34 J.s =1.062×1056 kg3/2/J3.s3 =6.81×1027 m-3.eV-2/3

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

NE=6.81×1027 m-3.eV-2/38eV1/2 =1.9×1028 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 1.9×1028 m-3.eV-1.

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