Introductory Chemistry: A Foundation - Zumdahl S.S., DeCoste D.J. 2019

Chemical Foundations: Elements, Atoms, and Ions
Isotopes

Objectives

· To learn about the terms isotope, atomic number, and mass number.

· To understand the use of the symbol to describe a given atom.

We have seen that an atom has a nucleus with a positive charge due to its protons and has electrons in the space surrounding the nucleus at relatively large distances from it.

As an example, consider a sodium atom, which has protons in its nucleus. Because an atom has no overall charge, the number of electrons must equal the number of protons. Therefore, a sodium atom has electrons in the space around its nucleus. It is always true that a sodium atom has protons and electrons. However, each sodium atom also has neutrons in its nucleus, and different types of sodium atoms exist that have different numbers of neutrons.

When Dalton stated his atomic theory in the early 1800s, he assumed all of the atoms of a given element were identical. This idea persisted for over a hundred years, until James Chadwick discovered that the nuclei of most atoms contain neutrons as well as protons. (This is a good example of how a theory changes as new observations are made.) After the discovery of the neutron, Dalton’s statement that all atoms of a given element are identical had to be changed to “All atoms of the same element contain the same number of protons and electrons, but atoms of a given element may have different numbers of neutrons.”

To illustrate this idea, consider the sodium atoms represented in Fig. 4.8. These atoms are isotopes , or atoms with the same number of protons but different numbers of neutrons. The number of protons in a nucleus is called the atom’s atomic number . The sum of the number of neutrons and the number of protons in a given nucleus is called the atom’s mass number . To specify which of the isotopes of an element we are talking about, we use the symbol

where

Figure 4.8.

Two isotopes of sodium. Both have protons and electrons, but they differ in the number of neutrons in their nuclei.

For example, the symbol for one particular type of sodium atom is written

The particular atom represented here is called sodium-23 because it has a mass number of . Let’s specify the number of each type of subatomic particle. From the atomic number we know that the nucleus contains protons. And because the number of electrons is equal to the number of protons, we know that this atom contains electrons. How many neutrons are present? We can calculate the number of neutrons from the definition of the mass number:

or, in symbols,

Chemistry in Focus “Whair” Do You Live?

Picture a person who has been the victim of a crime in a large city in the eastern United States. The person has been hit in the head and, as a result, has total amnesia. The person’s ID has been stolen, but the authorities suspect he may not be from the local area. Is there any way to find out where the person might be from? The answer is yes. Recent research indicates that the relative amounts of the isotopes of hydrogen and oxygen in a person’s hair indicate in which part of the United States a person lives.

Support for this idea has come from a recent study by James Ehleringer, a chemist at the University of Utah in Salt Lake City. Noting that the concentrations of hydrogen-2 (deuterium) and oxygen-18 in drinking water vary significantly from region to region in the United States (see accompanying illustration), Ehleringer and his colleagues collected hair samples from barbershops in cities and states. Their analyses showed that of the variations in the hydrogen and oxygen isotopes in the hair samples result from the isotopic composition of the local water. Based on their results, the group was able to develop estimates of the isotopic signature of individuals’ hair from various regions of the country. Although this method cannot be used to pinpoint a person’s place of residence, it can give a general region. This method might be helpful for the amnesia victim just described by showing where to look for his family. His picture could be shown on TV in the region indicated by analysis of his hair. Another possible use of this technique is identifying the country of origin of victims of a natural disaster in a tourist region with visitors from all over the world. In fact, a similar technique was used to specify the countries of origin of the victims of the tsunami that devastated southern Asia in December 2004.

An interesting verification of this technique occurred when the researchers examined a strand of hair from a person who had recently moved from Beijing, China, to Salt Lake City. Analysis of various parts of the hair showed a distinct change in isotopic distribution corresponding to his change of residence. Thus the isotopes of elements can provide useful information in unexpected ways.

See Problem 4.40

We can isolate (solve for) the number of neutrons by subtracting from both sides of the equation:

This is a general result. You can always determine the number of neutrons present in a given atom by subtracting the atomic number from the mass number. In this case , we know that and . Thus

In summary, sodium-23 has electrons, protons, and neutrons.

Interactive Example 4.2. Interpreting Symbols for Isotopes

In nature, elements are usually found as a mixture of isotopes. Three isotopes of elemental carbon are (carbon-12), (carbon-13), and (carbon-14). Determine the number of each of the three types of subatomic particles in each of these carbon atoms.

Solution

The number of protons and electrons is the same in each of the isotopes and is given by the atomic number of carbon, . The number of neutrons can be determined by subtracting the atomic number from the mass number :

The numbers of neutrons in the three isotopes of carbon are

In summary,

Self-Check: Exercise 4.2

· Give the number of protons, neutrons, and electrons in the atom symbolized by . Strontium-90 occurs in fallout from nuclear testing. It can accumulate in bone marrow and may cause leukemia and bone cancer.

See Problems 4.39 and 4.42.

Self-Check: Exercise 4.3

· Give the number of protons, neutrons, and electrons in the atom symbolized by .

See Problems 4.39 and 4.42.

Interactive Example 4.3. Writing Symbols for Isotopes

Write the symbol for the magnesium atom (atomic number ) with a mass number of . How many electrons and how many neutrons does this atom have?

Solution

The atomic number means the atom has protons. The element magnesium is symbolized by . The atom is represented as

and is called magnesium-24. Because the atom has protons, it must also have electrons. The mass number gives the total number of protons and neutrons, which means that this atom has neutrons .

© Cengage Learning

Magnesium burns in air to give a bright white flame.

Chemistry in Focus Isotope Tales

The atoms of a given element typically consist of several isotopes—atoms with the same number of protons but different numbers of neutrons. It turns out that the ratio of isotopes found in nature can be very useful in natural detective work. One reason is that the ratio of isotopes of elements found in living animals and humans reflects their diets. For example, African elephants that feed on grasses have a different ratio in their tissues than elephants that primarily eat tree leaves. This difference arises because grasses have a different growth pattern than leaves do, resulting in different amounts of and being incorporated from the in the air. Because leaf-eating and grass-eating elephants live in different areas of Africa, the observed differences in the isotope ratios in elephant ivory samples have enabled authorities to identify the sources of illegal samples of ivory.

Another case of isotope detective work involves the tomb of King Midas, who ruled the kingdom Phyrgia in the eighth century B.C. Analysis of nitrogen isotopes in the king’s decayed casket has revealed details about the king’s diet. Scientists have learned that the ratios of carnivores are higher than those of herbivores, which in turn are higher than those of plants. It turns out that the organism responsible for decay of the king’s wooden casket has an unusually large requirement for nitrogen. The source of this nitrogen was the body of the dead king. Because the decayed wood under his now-decomposed body showed a high ratio, researchers feel sure that the king’s diet was rich in meat.

A third case of historical isotope detective work concerns the Pueblo ancestor people (commonly called the Anasazi), who lived in what is now northwestern New Mexico between A.D. 900 and 1150. The center of their civilization, Chaco Canyon, was a thriving cultural center boasting dwellings made of hand-hewn sandstone and more than logs. The sources of the logs have always been controversial. Many theories have been advanced concerning the distances over which the logs were hauled. Recent research by Nathan B. English, a geochemist at the University of Arizona in Tucson, has used the distribution of strontium isotopes in the wood to identify the probable sources of the logs. This effort has enabled scientists to understand more clearly the Anasazi building practices.

These stories illustrate how isotopes can serve as valuable sources of biologic and historical information.

See Problem 4.41

Interactive Example 4.4. Calculating Mass Number

Write the symbol for the silver atom that has neutrons.

Solution

The element symbol is , where we know that . We can find from its definition, . In this case,

The complete symbol for this atom is .

Self-Check: Exercise 4.4

· Give the symbol for the phosphorus atom that contains neutrons.

See Problem 4.42.