Conceptual Questions

ssm Solution is in the Student Solutions Manual

| 1 | A material is known to be an isotope of lead, although the particular isotope is not known. From such limited information, which of the following quantities can you specify: (a) its atomic number, (b) its neutron number, (c) its atomic mass number? Explain.

| 2 | Two nuclei have different nucleon numbers and . Are the two nuclei necessarily isotopes of the same element? Give your reasoning.

| 3 | Two nuclei have the same radius, even though they contain different numbers of protons and different numbers of neutrons. Explain how this is possible.

| 4 | Using Figure 31-5, rank the following nuclei in ascending order (smallest first) according to the binding energy per nucleon: phosphorus , cobalt , tungsten , and thorium .

| 5 | Describe qualitatively how the radius of the daughter nucleus compares to that of the parent nucleus for (a) decay and (b) decay. Justify your answers in terms of Equation 31.2.

| 6 | Why do and decay produce new elements, but decay does not?

| 7 | ssm Uranium decays into thorium by means of decay, as Example 4 in the text discusses. A reasonable question to ask is, “Why doesn’t the nucleus just emit a single proton instead of an particle?” This hypothetical decay scheme is shown below, along with the pertinent atomic masses:

For a decay to be possible, it must bring the parent nucleus toward a more stable state by allowing the release of energy. Compare the total mass of the products of this hypothetical decay with the mass of and decide whether the emission of a single proton is possible for . Explain.

| 8 | Explain why unstable nuclei with short half-lives typically have only a small or zero natural abundance.

| 9 | The half-life of indium is . Thus, one-half of the nuclei in a sample of this isotope will decay in this time, which is very long. Is it possible for any single nucleus in the sample to decay after only one second? Justify your answer.

| 10 | (a) Is it possible for two different samples that contain different radioactive elements to have the same activity? (b) Is it possible for two different samples of the same radioactive element to have different activities? In each case, defend your answer.

| 11 | To which of the following objects, each about 1000 yr old, can the radiocarbon dating technique not be applied: a wooden box, a gold statue, and some plant seeds? Explain.

| 12 | Two isotopes have half-lives that are short, relative to the known age of the earth. Today, one of these isotopes is found in nature and one is not. How is this possible, considering that both should have long since decayed to zero? Explain.

| 13 | ssm Suppose there were a greater number of carbon atoms in a plant living 5000 yr ago than is currently believed. When the seeds of this plant are tested today using radiocarbon dating, is the age obtained too small or too large? Give your reasoning.

| 14 | Review Conceptual Example 12 as an aid in answering this question. Tritium is an isotope of hydrogen and undergoes decay with a half-life of 12.33 yr. Like carbon, tritium is produced in the atmosphere because of cosmic rays and can be used in a radioactive dating technique. Can tritium dating be used to determine a reliable date for a sample that is about 700 yr old? Account for your answer.

| 15 | Because of radioactive decay, one element can be transmuted into another. Thus, a container of uranium ultimately becomes a container of lead , as Figure 31-16 indicates. How long does the transmutation of entirely into require —several decades, several centuries, thousands of years, millions of years, or billions of years? State your reasoning.

| 16 | ssm In Figure 31-7 the trajectory of the particles has a greater curvature than that of the particles. Assuming that the speeds of the two types of particles are the same, explain why the curvatures are different. Consider the effects of both mass and charge.

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