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Chapter 4: Problem 98

Silicon has three naturally occurring isotopes: Si-28 with mass \(27.9769\) amu and a natural abundance of \(92.21 \%\), Si-29 with mass \(28.9765\) amu and a natural abundance of \(4.69 \%\), and Si-30 with mass \(29.9737\) amu and a natural abundance of \(3.10 \%\). Calculate the atomic mass of silicon.

Short Answer

Expert verified
The atomic mass of silicon is approximately 28.0855 amu.

Step by step solution

01

Convert Percent Abundances to Decimal Form

Convert the natural abundances of the isotopes of silicon from percentages to decimals by dividing each by 100.
02

Multiply the Mass of Each Isotope by Its Decimal Abundance

Calculate the weighted mass of each isotope by multiplying the mass of each isotope by its corresponding decimal abundance.
03

Add the Weighted Masses Together

Sum the weighted masses of all the isotopes to obtain the average atomic mass of silicon.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Isotope Abundance
Understanding isotope abundance is essential when calculating the atomic mass of an element. Isotopes are atoms of the same element that contain the same number of protons but differ in the number of neutrons. Therefore, they have different mass numbers.

For a given element, natural abundance refers to the percentage of each isotope found in nature. To find the average atomic mass, we must consider these abundances. For instance, in a sample of silicon, you may find mainly Si-28 because it has the highest natural abundance. The natural abundances are crucial as they weigh in the mass of each isotope in the final average atomic mass calculation.
Atomic Mass Unit (amu)
The atomic mass unit (amu) is a standard unit of mass that quantifies the mass of atoms or molecules. It's defined as one twelfth of the mass of a carbon-12 atom. Since atoms are incredibly small and their masses are extremely light, the amu provides a convenient way to express their masses.

In the case of silicon's isotopes, the mass of Si-28 is given as 27.9769 amu, which indicates it is slightly lighter than 28 times the mass of carbon-12's standard reference. The precision of these measurements is vital, as they are used to calculate the average atomic mass of elements.
Silicon Isotopes
Silicon, like all elements, has several isotopes. As mentioned in the exercise, silicon mainly exists in nature as three isotopes: Si-28, Si-29, and Si-30. These isotopes have slightly different masses but identical chemical properties.

The difference in mass stems from the number of neutrons in the nucleus. This diversity in mass allows us to study and utilize the unique properties of each isotope in various scientific and technological applications, particularly in semiconductor technology and materials science.
Chemical Elements
Chemical elements are pure substances consisting of only one type of atom characterized by a specific number of protons in their nuclei, known as the atomic number. While the number of protons (and electrons) defines the element, the number of neutrons can vary, leading to the formation of different isotopes.

Each element has a unique place on the periodic table, with its chemical behavior dictated by its atomic structure. Despite the nuances of isotopes, these atomic variations do not change the fundamental chemical nature of the element.
Average Atomic Mass
The average atomic mass of an element is the weighted average of the masses of its isotopes, based on their natural abundance. It's a reflection of the mass of an element if you picked a random atom of it from a large sample where all isotopes are mixed as they naturally occur.

Mathematically, this is calculated by multiplying the mass of each isotope by its decimal abundance and summing these products together. The result is an average mass that closely matches the mass you would find if you averaged the mass of a significant number of atoms of that element.

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Most popular questions from this chapter

What are the properties of metals? Where are metals found on the periodic table?

Which statements are consistent with Dalton's atomic theory as it was originally stated? Explain your answers. (a) Calcium and titanium atoms have the same mass. (b) Neon and argon atoms are the same. (c) All cobalt atoms are identical. (d) Sodium and chlorine atoms combine in a \(1: 1\) ratio to form sodium chloride.

Electrical charge is sometimes reported in coulombs (C). On this scale, 1 electron has a charge of \(-1.6 \times 10^{-19} \mathrm{C}\). Suppose your body acquires \(-125 \mathrm{mC}\) (millicoulombs) of charge on a dry day. How many excess electrons has it acquired? (Hint: Use the charge of an electron in coulombs as a conversion factor between charge and number of electrons.)

Locate each group on the periodic table and list the charge of the ions it tends to form. (a) Group 1A (b) Group 2A (c) Group 3A (d) Group 6A (e) Group 7A

Is matter usually charge-neutral? How would matter be different if it were not charge-neutral?
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