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
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) =
2) Given:
Five option to select from to answer the question regarding adjacent energy levels.
3) Equations
P(E) =
4) Calculations
The highest occupied band in a metal is the
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?
Chapter 41 Solutions
FUNDAMENTALS OF PHYSICS V.1
- 19:39 · C Chegg 1 69% ✓ The compound beam is fixed at Ę and supported by rollers at A and B. There are pins at C and D. Take F=1700 lb. (Figure 1) Figure 800 lb ||-5- F 600 lb بتا D E C BO 10 ft 5 ft 4 ft-—— 6 ft — 5 ft- Solved Part A The compound beam is fixed at E and... Hình ảnh có thể có bản quyền. Tìm hiểu thêm Problem A-12 % Chia sẻ kip 800 lb Truy cập ) D Lưu of C 600 lb |-sa+ 10ft 5ft 4ft6ft D E 5 ft- Trying Cheaa Những kết quả này có hữu ích không? There are pins at C and D To F-1200 Egue!) Chegg Solved The compound b... Có Không ☑ ||| Chegg 10 וחarrow_forwardNo chatgpt pls will upvotearrow_forwardNo chatgpt pls will upvotearrow_forward
- No chatgpt pls will upvotearrow_forwardair is pushed steadily though a forced air pipe at a steady speed of 4.0 m/s. the pipe measures 56 cm by 22 cm. how fast will air move though a narrower portion of the pipe that is also rectangular and measures 32 cm by 22 cmarrow_forwardNo chatgpt pls will upvotearrow_forward
- 13.87 ... Interplanetary Navigation. The most efficient way to send a spacecraft from the earth to another planet is by using a Hohmann transfer orbit (Fig. P13.87). If the orbits of the departure and destination planets are circular, the Hohmann transfer orbit is an elliptical orbit whose perihelion and aphelion are tangent to the orbits of the two planets. The rockets are fired briefly at the depar- ture planet to put the spacecraft into the transfer orbit; the spacecraft then coasts until it reaches the destination planet. The rockets are then fired again to put the spacecraft into the same orbit about the sun as the destination planet. (a) For a flight from earth to Mars, in what direction must the rockets be fired at the earth and at Mars: in the direction of motion, or opposite the direction of motion? What about for a flight from Mars to the earth? (b) How long does a one- way trip from the the earth to Mars take, between the firings of the rockets? (c) To reach Mars from the…arrow_forwardNo chatgpt pls will upvotearrow_forwarda cubic foot of argon at 20 degrees celsius is isentropically compressed from 1 atm to 425 KPa. What is the new temperature and density?arrow_forward
- Calculate the variance of the calculated accelerations. The free fall height was 1753 mm. The measured release and catch times were: 222.22 800.00 61.11 641.67 0.00 588.89 11.11 588.89 8.33 588.89 11.11 588.89 5.56 586.11 2.78 583.33 Give in the answer window the calculated repeated experiment variance in m/s2.arrow_forwardNo chatgpt pls will upvotearrow_forwardCan you help me solve the questions pleasearrow_forward
- Modern PhysicsPhysicsISBN:9781111794378Author:Raymond A. Serway, Clement J. Moses, Curt A. MoyerPublisher:Cengage LearningPhysics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning