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Sears and Zemansky's University Physics with Modern Physics | 13th Edition | ISBN: 9780321696861 | Authors: Hugh D. Young; Roger A. Freedman; A. Lewis Ford
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Solved: Metallic lithium has a bcc crystal structure. Each

Chapter 42, Problem 53P

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QUESTION:

Problem 53P

Metallic lithium has a bcc crystal structure. Each unit cell is a cube of side length a = 0.35 nm. (a) For a bcc lattice, what is the number of atoms per unit volume? Give your answer in terms of a. (Hint: How many atoms are there per unit cell?) (b) Use the result of part (a) to calculate the zero-temperature Fermi energy EF0 for metallic lithium. Assume there is one free electron per atom.

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QUESTION:

Problem 53P

Metallic lithium has a bcc crystal structure. Each unit cell is a cube of side length a = 0.35 nm. (a) For a bcc lattice, what is the number of atoms per unit volume? Give your answer in terms of a. (Hint: How many atoms are there per unit cell?) (b) Use the result of part (a) to calculate the zero-temperature Fermi energy EF0 for metallic lithium. Assume there is one free electron per atom.

ANSWER:

Introduction

First we have to calculate the number of electrons per unit volume for the metallic lithium and then we have to calculate the zero temperature fermi energy.

Step 1

(a) The number of atoms in a BCC crystal is  per unit cells.

The volume of one unit cell is given

Hence the number of atoms per unit cell is given by

Now we have

,

Hence

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