Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 10: Q50E (page 469)

Assuming an interatomic spacing of 0.15 nm, obtain a rough value for the width (in eV) of then=2 band in a one-dimensional crystal.

Short Answer

Expert verified

The estimated value of the band width is 50 eV.

Step by step solution

01

Determine the formulas

Consider the relation between the wave numbers and the energy as follows:

E=h2k22m

Here, E is the energy, m is the effective mass, h is the planck’s constant and k is the wave number.

02

Determine the value of the width as:

Consider the formula for the change in energy as:

ΔE=E2−E1=h22m(k22−k12)

Substitute the values and solve as:

ΔE=h22m((2πa2)−(πa2))=h22m(3πa2)=3h2π22ma2

Solve further as:

ΔE=3(1.055×10−34 Js)(π2)2(9.11×10−31 kg)(0.15×10−9 m)2=50 eV

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Based only on the desire to limit minority carriers, why would silicon be preferable to germanium as a fabric for doped semiconductors?

Question: Referring to equations(10-2), lobe I of the hybrid states combines the spherically symmetric s state with the state that is oriented along thez-axis. and thus sticks out in the direction (see Exercises 28 and 33), If Figure is a true picture, then in a coordinate system rotated counterclockwise about they-axis by the tetrahedral angle, lobe II should become lobe. In the new frame. -values are unaffected. but what had been values in the 2x -plane become values in the -plane. according tox=x'cosα+z'sinα and z'cosα-x'sinα, whereα=109.5o iscos-1(-13) , or .

(a) Show that lobe II becomes lobe I. Note that since neither the 2s state nor the radial part of the p states is affected by a rotation. only the angular parts given in equations (10-1) need be considered.

(b) Show that if lobe II is instead rotated about thez-axis by simply shifting φby±1200 . it becomes lobes III and IV.

Question:If electrical conductivity were determined by the mere static presence of positive ions rather than by their motion the collision time would be inversely proportional to the electron's average speed. If however, it were dominated by the motion of the ions, it should be inversely proportional to the “area" presented by a jiggling ion, which is in turn proportional to the square of its amplitude as an oscillator. Argue that only the latter view gives the correct temperature dependence in conductors of σ∝T-1. Use the equipartition theorem (usually covered in introductory thermodynamics and also discussed in Section 9.9).

From the diagrams in Figure 7.15and the qualitative behavior of the wave functions they represent, argue that a combination of the2pZ(i.e.,ml=0) and the negative of the 2swould produce a function that sticks out preferentially in the positive Zdirection. This is known as a hybridspstate.

Question: The critical temperature lead is 7.2 K. What is the binding energy of its Cooper pairs at zero temperature?
See all solutions

Recommended explanations on Physics Textbooks

Famous Physicists

Read Explanation

Conservation of Energy and Momentum

Read Explanation

Rotational Dynamics

Read Explanation

Electric Charge Field and Potential

Read Explanation

Physical Quantities And Units

Read Explanation

Classical Mechanics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free