   # Mass spectrometric analysis showed that there are four isotopes of an unknown element having the following masses and abundances: Three elements in the periodic table that have atomic weights near these values are lanthanum (La), atomic number 57, atomic weight 138.9055; cerium (Ce), atomic number 58, atomic weight 140.115; and praseodymium (Pr), atomic number 59, atomic weight 140.9076. Using the data above, calculate the atomic weight, and identify the element if possible. ### Chemistry & Chemical Reactivity

9th Edition
John C. Kotz + 3 others
Publisher: Cengage Learning
ISBN: 9781133949640

#### Solutions

Chapter
Section ### Chemistry & Chemical Reactivity

9th Edition
John C. Kotz + 3 others
Publisher: Cengage Learning
ISBN: 9781133949640
Chapter 2, Problem 154GQ
Textbook Problem
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## Mass spectrometric analysis showed that there are four isotopes of an unknown element having the following masses and abundances: Three elements in the periodic table that have atomic weights near these values are lanthanum (La), atomic number 57, atomic weight 138.9055; cerium (Ce), atomic number 58, atomic weight 140.115; and praseodymium (Pr), atomic number 59, atomic weight 140.9076. Using the data above, calculate the atomic weight, and identify the element if possible.

Interpretation Introduction

Interpretation: The average atomic mass and the elements are needed to be determined from the given data’s.

Concept introduction:

Equation for average weight is

average mass=(%abundanceisotop-1100)×(massofisotop-1) +(%abundanceisotop-2100)×(massofisotop-2)+etc

Mass: It is the quantitative measure of a substance. The amount of matter present in substance is expressed as mass. The S.I. unit of mass is kg.

### Explanation of Solution

There are four isotopes for the element.

The mass of isotope-1 is 135.9090u and its abundance is 0.193%.

The mass of isotope-2 is 137.9057u and its abundance is 0.250%.

The mass of isotope-3 is 139.9053u and its abundance is 88.48%.

The mass of isotope-4 is 141.9090u and its abundance is 11.07%.

Equation for average weight is,

average weight=(%abundanceisotop-1100)×(massofisotop-1) +(%abundanceisotop-2100)×(mass

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