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Chapter 41: Q52P (page 1275)

Verify the numerical factor 0.121 in Eq. 41-9.

Short Answer

Expert verified

The numerical factor 3162π2/3is equal to the numerical factor 0.121.

Step by step solution

01

The given data

The equation of Fermi energy according to Eq. 41-9 is

EF=3162π2/3h2mn2/3.

where, n is the number of conduction electrons per unit volume, m is the mass of an electron and h is the Planck’s constant.

02

Understanding the concept of Fermi energy

The highest level to be occupied by the electron in the valence band at 0 K is known as Fermi level.

03

Calculation of verifying the numerical factor 0.121

From the given Fermi energy equation, the numerical constant value is given by,

c=3162π2/3=4.22×10-22/3=0.121

Hence, the numerical factor 0.121 is verified.

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Most popular questions from this chapter

On which of the following does the interval between adjacent energy levels in the highest occupied band of a metal depend: (a) the material of which the sample is made, (b) the size of the sample, (c) the position of the level in the band, (d) the temperature of the sample, (e) the Fermi energy of the metal?

Figure 41-21 shows three leveled levels in a band and also the Fermi level for the material. The temperature is 0K. Rank the three levels according to the probability of occupation, greatest first if the temperature is (a) 0K and (b) 1000K. (c) At the latter temperature, rank the levels according to the density of states N(E) there, greatest first.

Use Eq. 41-9 to verify 7.0eV as copper’s Fermi energy.

A certain metal has 1.70×1028 conduction electrons per cubic meter. A sample of that metal has a volume of 6.00×10-6m3and a temperature of 200K. How many occupied states are in the energy range of3.20x10-20J that is centered on the energy4.00x10-19J? (Caution:Avoid round-off in the exponential.)

The occupancy probability function (Eq. 41-6) can be applied to semiconductors as well as to metals. In semiconductors the Fermi energy is close to the midpoint of the gap between the valence band and the conduction band. For germanium, the gap width is 0.67eV. What is the probability that (a) a state at the bottom of the conduction band is occupied and (b) a state at the top of the valence band is not occupied? Assume that T = 290K. (Note:In a pure semiconductor, the Fermi energy lies symmetrically between the population of conduction electrons and the population of holes and thus is at the center of the gap. There need not be an available state at the location of the Fermi energy.)
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