   Chapter 1, Problem 61RGQ

Chapter
Section
Textbook Problem

Copper:(a) Suppose you have a cube of copper metal that is 0.236 cm on a side with a mass of 0.1206 g. If you know that each copper atom (radius = 128 pm) has a mass of 1.055 × 10–22 g (you will learn in Chapter 2 how to find the mass of one atom), how many atoms are there in this cube? What fraction of the cube is filled with atoms? (Or conversely, how much of the lattice is empty space?) Why is there “empty” space in the lattice?(b) Now look at the smallest, repeating unit of the crystal lattice of copper. Knowing that an edge of this cube is 361.47 pm and the density of copper is 8.960 g/cm3, calculate the number of copper atoms in this smallest, repeating unit.

(a)

Interpretation Introduction

Interpretation:

The number of atoms and the fraction of cube filled in the atoms has to be given.  The reason for the empty space in the lattice has to be explained.

Explanation

The number of atoms and the fraction of cube filled is calculated as,

Calculate the number of copper atoms:_Known: Number of atoms = 0.1206 g1.055×10-22= 1.14×1021 atomsCalculate the fraction of cube filled with atoms:_Total V of atoms = 43π(128×10-12)3m31atom×1

(b)

Interpretation Introduction

Interpretation:

The number of atoms in the smallest repeating unit has to be calculated.

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