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Chapter 41: Q26P (page 1273)

At T = 300K, how far above the Fermi energy is a state for which the probability of occupation by a conduction electron is 0.10?

Short Answer

Expert verified

The value of the energy of the state above the Fermi energy is 9.1×10-21J9.1 .

Step by step solution

01

The given data

a) The temperature value, T = 300 K

b) The probability value, P (E) = 0.10

02

Understanding the concept of energy state

Using the equation of occupancy probability for an energy state, we can get the value of the energy that is above the level of the Fermi energy.

Formula:

The probability of the condition that a particle will have energy E according to Fermi-Dirac statistics, PE=1eE1-EF/kT+1wherek=1.38×10-23J/K (i)

03

Calculation of the value of energy above Fermi level

Let the energy of the state in the problem be an amount ∆Eabove the Fermi levelEF.

Then, the equation of the required energy can be given using the occupancy probability of equation (i) and the given data as follows:

PE=1e∆E/kT+1∆E=kTIn1PE-1=1.38×10-23J/K300KIn10.1-1=9.1×10-21J

Hence, the value of the energy is 9.1×10-21J.

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Most popular questions from this chapter

Consider a copper wire that is carrying, say, a few amperes of current. Is the drift speed vdof the conduction electrons that form that current about equal to, much greater than, or much less than the Fermi speed vFfor copper (the speed associated with the Fermi energy for copper)?

Assume that the total volume of a metal sample is the sum of the volume occupied by the metal ions making up the lattice and the (separate) volume occupied by the conduction electrons. The density and molar mass of sodium (a metal) are 971kg/m3and 23.g/mol, respectively; assume the radius of the Na+ ion is . (a) What percent of the volume of a sample of metallic sodium is occupied by its conduction electrons? (b) Carry out the same calculation for copper, which has density, molar mass, and ionic radius of 8960kg/m3, 63.5g/mol, and 135 pm, respectively. (c) For which of these metals do you think the conduction electrons behave more like a free-electron gas?

(a) What maximum light wavelength will excite an electron in the valence band of diamond to the conduction band? The energy gap is 5.50 eV. (b) In what part of the electromagnetic spectrum does this wavelength lie?

What is the probability that a state 0.0620eV above the Fermi energy will be occupied at (a) T = OK and (b) T = 320K?

Pure silicon at room temperature has an electron number density in the conduction band of about 5.00×1015m-3and an equal density of holes in the valence band. Suppose that one of every 107silicon atoms is replaced by a phosphorus atom. (a) Which type will the doped semiconductor be, nor p? (b) What charge carrier number density will the phosphorus add? (c) What is the ratio of the charge carrier number density (electrons in the conduction band and holes in the valence band) in the doped silicon to that in pure silicon?
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