Fundamentals of Physics Extended
Fundamentals of Physics Extended
10th Edition
ISBN: 9781118230725
Author: David Halliday, Robert Resnick, Jearl Walker
Publisher: Wiley, John & Sons, Incorporated
Question
Book Icon
Chapter 41, Problem 1Q
To determine

To select correct options:

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

Expert Solution & Answer
Check Mark

Answer to Problem 1Q

Solution:

The interval between adjacent energy levels in the highest occupied band of a metal depend on

(b) the size of the sample

(c) the position of the level in the band

(d) the temperature of the sample.

Explanation of Solution

Explanations

1) Concept

An isolated atom can exist in only a discrete set of energy levels. As atoms come together to form a solid, the levels of the individual atoms merge to form the energy bands. An energy band is made up of an enormous number of very closely spaced levels.

The density of occupied states No(E) is given by the product of two quantities P(E) and N(E).

No(E) = P(E) x N(E)

P(E) is the probability of occupancy. And N(E) is the number of energy levels per unit volume of the sample per unit energy.

P(E) = 1e(E-Ef)kT+1

2) Given:

Five option to select from to answer the question regarding adjacent energy levels.

3) Equations

P(E) = 1e(E-Ef)kT+1

4) Calculations

The highest occupied band in a metal is the conduction band.

The interval between adjacent energy levels in a conduction band will depend on N(E) and the number of electrons – which means it will depend on the size of the sample. This implies that option (b) is correct.

Probability of occupancy P(E), and N(E) both depend on energy E – that is the position of the energy level in the band. This implies that option (c) is correct.

In addition, we see that the energy levels are dependent on temperature T. Also thermal expansion and contraction of metals, will increase or decrease the electron energy overlaps, and hence the adjacent energy levels.

Conclusion

The free electrons in a metal fill up the conduction band. But all energy levels including adjacent energy levels are closely spaced levels due to the Pauli Exclusion Principle.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
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?
A certain bivalent metal has a density of 6.906 g/cm3 and a molar mass of 97.8 g/mol. Calculate (a) the number density of conduction electrons, (b) the Fermi energy, (c) the Fermi speed, and (d) the de Broglie wavelength corresponding to this electron speed.
The Fermi energy of copper at 300 K is 7.05 eV. (a) What is the average energy of a conduction electron in copper at 300 K? (b) At what temperature would the average translational energy of a molecule in an ideal gas be equal to the energy calculated in part (a)?
Knowledge Booster
Background pattern image
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Modern Physics
Physics
ISBN:9781111794378
Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher:Cengage Learning
Text book image
Physics for Scientists and Engineers with Modern ...
Physics
ISBN:9781337553292
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning