   Chapter 3, Problem 42E

Chapter
Section
Textbook Problem

Assume silicon has three major isotopes in nature as shown in the table below. Fill in the missing information. Isotope Mass (u) Abundance 28Si 27.98 _____ 29Si ____ 4.70% 30Si 29.97 3.09%

Interpretation Introduction

Interpretation: The mass and percentage abundance of silicon isotope is missing in the given table. These missing information are to be filled in the given table.

Concept introduction: The elements having same atomic number but different mass number are called isotopes of that element.

The atomic mass is defined as the sum of number of protons and number of neutrons. If the percentage composition is given, then atomic mass can be calculated by multiplying the mass of element with its percentage composition.

Average atomic mass is defined as the percentage sum of atomic mass of individual atom.

Average atomic mass=Percentageabundanceofeachisotopes×atomicmassofthatisotope

Explanation

To determine: The percentage abundance of 28Si .

Given

The percentage abundance of 29Si is 4.70% .

The percentage abundance of 30Si is 3.09% .

The total percentage abundance of all the three isotopes is 100% . Therefore,

The percentage abundance of isotope 28Si is calculated as,

28Si%+29Si%+30Si%=100%

Substitute the value of 29Si% and 30Si% in above equation.

28Si%+4.70%+3.09%=100%28Si%=92.21%_

The percentage abundance of 28Si is 92.21%_ .

To determine: The mass of isotope 29Si .

Given

Mass of isotope 28Si is 27.98u .

Abundance of isotope 29Si is 4.70% .

Mass of isotope 30Si is 29.97u .

Abundance of isotope 30Si is 3.09% .

The average atomic mass of silicon (Si) is 28.09u .

Formula

The average atomic mass is calculated using the formula,

Average atomic mass=Percentageabundanceofeachisotopes×atomicmassofthatisotope

Substitute the value of average atomic mass, percentage abundance of isotopes of silicon (Si) and their atomic mass in above equation.

Average atomic mass(Si)=(92

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