Book edition 10th Edition

Author(s) David Halliday

Pages 1328 pages

ISBN 9781118230718

Answers without the blur.

Just sign up for free and you're in.

Short Answer

Figure 41-1a shows 14 atoms that represent the unit cell of copper. However, because each of these atoms is shared with one or more adjoining unit cells, only a fraction of each atom belongs to the unit cell shown. What is the number of atoms per unit cell for copper? (To answer, count up the fractional atoms belonging to a single unit cell.)

The number of atoms per unit cell is 4.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: The given data

The unit cell of the copper shows the representation of 14 atoms.

Step 2: Understanding the concept of lattice structure of copper

A lattice structure is a three-dimension open structure that is made up of more than one repeating unit cell of an atom. The cells define the connectivity of the constituent atoms in the unit cell structure. They can be of mainly four types of lattice structures: FCC, BCC, HCP, and simple cubic. Now, here the given unit cell of copper has an FCC structure. The total number of atoms per unit cell is calculated by calculating the atoms’ contributions that are placed at the corners and face constituting the structure.

Step 3: Calculation of the number of atoms per unit cell

As the lattice structure copper consisting of 14 electrons is an FCC structure, thus the contribution to the structure is only from the face and corner atoms.

The contribution of each corner atom per unit cell of copper is $\frac{1}{8}$ . So, the total contribution by 8 corner atoms is 1.

The contribution of each face atom per unit cell of copper is $\frac{1}{2}$ . Thus, the contribution of 6 face atoms per unit cell of copper is 3.

Now, the total contribution of the FCC lattice in the copper unit cell is given by:

$(\frac{1}{8} \times 8) + (\frac{1}{2} \times 6) = 4$

Hence, the number of atoms per unit cell of copper is 4.

Find Study Materials for

Create Study Materials

Select your language

Fundamentals Of Physics

Answers without the blur.

Short Answer

Step by Step Solution

Step 1: The given data

Step 2: Understanding the concept of lattice structure of copper

Step 3: Calculation of the number of atoms per unit cell

Most popular questions for Physics Textbooks

Want to see more solutions like these?

Recommended explanations on Physics Textbooks

Select your language

Fundamentals Of Physics

Answers without the blur.

Short Answer

Step by Step Solution

Step 1: The given data

Step 2: Understanding the concept of lattice structure of copper

Step 3: Calculation of the number of atoms per unit cell

Most popular questions for Physics Textbooks

Want to see more solutions like these?

Recommended explanations on Physics Textbooks

Work Energy and Power

Radiation

Astrophysics

Physics of Motion

Scientific Method Physics

Fluids

Torque and Rotational Motion

Nuclear Physics

Fields in Physics

Measurements

Space Physics

Electricity

Physical Quantities and Units

Medical Physics

Electrostatics

Further Mechanics and Thermal Physics

Mechanics and Materials

Engineering Physics

Energy Physics

Force

Particle Model of Matter

Waves Physics

Magnetism

Modern Physics

Atoms and Radioactivity

Dynamics

Electricity and Magnetism

Conservation of Energy and Momentum

Fundamentals of Physics

Kinematics Physics

Circular Motion and Gravitation

Linear Momentum

Rotational Dynamics

Oscillations

Translational Dynamics

Geometrical and Physical Optics

Thermodynamics

Magnetism and Electromagnetic Induction

Electromagnetism

Electric Charge Field and Potential

Turning Points in Physics