Fundamentals of Physics Extended 10e Binder Ready Version + WileyPLUS Registration Card
Fundamentals of Physics Extended 10e Binder Ready Version + WileyPLUS Registration Card
10th Edition
ISBN: 9781118732090
Author: David Halliday
Publisher: Wiley (WileyPLUS Products)
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
suggest a reason ultrasound cleaning is better than cleaning by hand?
Checkpoint 4 The figure shows four orientations of an electric di- pole in an external electric field. Rank the orienta- tions according to (a) the magnitude of the torque on the dipole and (b) the potential energy of the di- pole, greatest first. (1) (2) E (4)
What is integrated science. What is fractional distillation What is simple distillation
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