Solution Manual for Materials Science and Engineering An Introduction 10th by Callister

SOLUTION MANUAL




SOLUTION MANUAL

, CHAPTER 2


ATOMIC STRUCTURE AND INTERATOMIC BONDING


PROBLEM SOLUTIONS




Fundamental Concepts
Electrons in Atoms


2.1 Cite the difference between atomic mass and atomic weight.

Solution

Atomic mass is the mass of an individual atom, whereas atomic weight is the average (weighted) of the
atomic masses of an atom's naturally occurring isotopes.

, 2.2 Chromium has four naturally-occurring isotopes: 4.34% of 50Cr, with an atomic weight of 49.9460 amu,
83.79% of 52Cr, with an atomic weight of 51.9405 amu, 9.50% of 53Cr, with an atomic weight of 52.9407 amu, and
2.37% of 54Cr, with an atomic weight of 53.9389 amu. On the basis of these data, confirm that the average atomic
weight of Cr is 51.9963 amu.

Solution

The average atomic weight of chromium is computed by adding fraction-of-occurrence/atomic weight

products for the three isotopes. Thus

, 2.3 Hafnium has six naturally occurring isotopes: 0.16% of 174Hf, with an atomic weight of 173.940 amu;

5.26% of 176Hf, with an atomic weight of 175.941 amu; 18.60% of 177Hf, with an atomic weight of 176.943 amu;

27.28% of 178Hf, with an atomic weight of 177.944 amu; 13.62% of 179Hf, with an atomic weight of 178.946 amu;.

and 35.08% of 180Hf, with an atomic weight of 179.947 amu. Calculate the average atomic weight of Hf.


Solution
The average atomic weight of halfnium is computed by adding fraction-of-occurrence—atomic weight

products for the six isotopes—i.e., using Equation 2.2. (Remember: fraction of occurrence is equal to the percent of

occurrence divided by 100.) Thus




Including data provided in the problem statement we solve for as




= 178.485 amu