1 1 What Is Radioactivity?
Name CHAPTER 10
Class
Date
Nuclear Changes
SECTION
1 What Is Radioactivity?
KEY IDEAS As you read this section, keep these questions in mind:
• What is radioactivity? • What are the different types of nuclear radiation? • How does nuclear decay change an atom?
What Is Radioactivity? Our lives are affected by radioactivity, or nuclear radiation, in many ways. Technology that uses radioactivity has helped people detect disease, kill cancer cells, and generate electricity. However, too much nuclear radiation can be harmful. We need to know where radiation exists and how to protect ourselves from it. First, we need to know what radioactivity is.
READING TOOLBOX Compare As you read, make a table that compares the main types of nuclear radiation. In the table, describe their similarities and differences.
What Happens During Nuclear Decay? Recall that an element may be found in different forms called isotopes. Isotopes of an element have the same number of protons in their nuclei but different numbers of neutrons. In contrast, different elements have different numbers of protons in their nuclei. Certain isotopes of some elements go through a process called radioactive decay. During radioactive decay, an unstable atom releases energy or particles from its nucleus. Sometimes, decay must happen many times before a nucleus is stable. After radioactive decay, the element may change into a different isotope of the same element or into a completely different element. The energy and matter released by the nuclei of unstable isotopes is called nuclear radiation.
This diagram shows what happens when a particular unstable isotope emits, or gives off, nuclear radiation. This nucleus is emitting both energy and a particle.
READING CHECK 1. Describe What happens during radioactive decay?
Electron Gamma ray
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What Is Radioactivity? continued
What Are Different Types of Nuclear Radiation? There are four main types of nuclear radiation: alpha particles, beta particles, gamma rays, and neutrons. Nuclear radiation can interact with nearby matter. The charge, mass, and energy of nuclear radiation determine how it will interact with matter. Types of Nuclear Radiation Radiation type
Symbol
Mass (kg)
Charge
Alpha particle
4 2
6.646 × 10−27
+2
Beta particle
0 –1
9.109 × 10−31
−1, (+1)
none
0
1.675 × 10−27
0
He
e,
0 +1
Graphic
e
EHHDBG@<EHL>K 2. Identify Which type of radiation has the most massive particles?
Gamma ray γ
3. Identify Which two types of radiation have no charge?
Neutron
0 1
n
ALPHA PARTICLES
READING CHECK 4. Identify Which element has the same number of protons and neutrons as an alpha particle?
Ernest Rutherford discovered the alpha particle while studying the decay of uranium-238, a radioactive isotope. Rutherford named the radiation alpha (α) rays after the first letter of the Greek alphabet. Later, he discovered that alpha rays were actually particles. Alpha particles are positively charged particles made of two protons and two neutrons—the same makeup as a helium nucleus. Alpha particles do not travel far through materials. In fact, they can barely pass through a sheet of paper. Two factors limit an alpha particle’s ability to pass through materials. First, alpha particles are more massive than other types of nuclear radiation. Second, because alpha particles are charged, they remove electrons from, or ionize, matter as they pass through it. This process causes the alpha particle to lose energy and slow down.
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What Is Radioactivity? continued
BETA PARTICLES
Some decaying nuclei emit a type of nuclear radiation that travels farther through matter than alpha particles do. This nuclear radiation is made up of beta particles, which are named after the second Greek letter, beta (β). Beta particles are typically fast moving electrons. However, beta particles can also be positively charged particles called positrons. Positrons have the same mass as electrons. Scientists wondered how negatively charged beta particles could come from a positively charged nucleus. A theory introduced in the 1930s helped explain this. Recall that a neutron has no charge. Scientists found that a neutron decays to form a proton and an electron. The nucleus then ejects, or shoots out, an electron at a high speed as a beta particle. GAMMA RAYS
Unlike alpha or beta particles, gamma rays are not made of matter and do not have an electric charge. Instead, gamma rays are a form of electromagnetic energy, or light. Gamma rays are named for the third Greek letter, gamma (γ). Like visible light and X rays, gamma rays consist of energy packets called photons. Gamma rays, however, have much more energy than light or X rays do. Although gamma rays have no electric charge, they can ionize matter easily and cause damage. Clothing or most building materials cannot stop gamma rays. Thus, gamma rays are more dangerous to the health of living things than alpha or beta particles are. Alpha particles
Beta particles
READING CHECK 5. Explain How is it possible for a positively charged nucleus to release a negatively charged beta particle?
Gamma rays
EHHDBG@<EHL>K A thin sheet of paper can block alpha particles.
About 3 mm of aluminum can block beta particles.
Seven cm or more of lead are needed to block gamma rays.
6. Identify Which of the three materials shown in the figure can block alpha particles, beta particles, and gamma rays?
Different kinds of nuclear radiation can pass through, or penetrate, different materials. Copyright © by Holt, Rinehart and Winston. All rights reserved.
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What Is Radioactivity? continued
What Is Neutron Emission?
READING CHECK 7. Identify What is one cause of neutron emission?
During neutron emission, a nucleus releases neutrons. Several processes may cause neutron emission. For example, sometimes, neutrons are released when atoms are hit by large particles such as alpha particles or other neutrons. Recall that charged particles can ionize matter. Because neutrons have no charge, they do not ionize matter. Neutrons don’t lose energy ionizing matter as alpha and beta particles do. Thus, neutrons travel farther through matter than either alpha or beta particles do.
How Does Nuclear Decay Change an Atom?
READING CHECK 8. Explain Why does alpha or beta decay cause an atom to become a different element?
Nuclear decay causes changes in the nucleus of an atom. When an unstable nucleus releases an alpha or beta particle, the number of protons and neutrons changes. For instance, when radium-226 emits an alpha particle, it changes to radon-222. Nuclear decay changed the number of protons, so the atom becomes a different element. Nuclear-decay equations are written in a way similar to chemical reaction equations. The original nucleus is like a reactant, so it is placed on the left side of the equation. The products of the reaction are placed on the right side of the equation.
What Happens During Alpha Decay?
EHHDBG@<EHL>K 9. Identify What is the atomic number of radon, Rn? How many protons does an atom of radon have?
10. Identify How many neutrons are in an atom of 222 86Rn?
During alpha decay, a large unstable nucleus becomes smaller by emitting an alpha particle. Recall that an alpha particle is the same as the nucleus of a helium atom. The equation for alpha decay shows that the atomic mass decreases by four and the atomic number decreases by two. The equation that describes the alpha decay of radium-226 is shown below. 226 88
Ra
222 86
Rn + 42 He
226 = 222 + 4 88 = 86 + 2
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What Is Radioactivity? continued
MASS NUMBER AND ATOMIC NUMBER
The mass number of the radium atom before decay is 226. This number is the same as the sum of the mass numbers of the decay products. Similarly, the radium atom has 88 protons before alpha decay. This number is the same as the sum of the protons produced by the decay.
What Happens During Beta Decay? During beta decay, the mass number of an atom before and after the decay will not change. However, the atomic number after the decay increases or decreases by one. Remember that the atomic number is equal to the number of protons. Recall that the number of protons an atom has determines what element that atom belongs to. Therefore, the atom after beta decay will change to a different element. Carbon-14 nucleus
EHHDBG@<EHL>K
Nitrogen-14 nucleus Beta particle (electron)
11. Explain After beta decay, why is the atom a different element?
During beta decay, a neutron in the nucleus decays to form a proton and an electron. The electron is emitted from the nucleus, but the proton stays. Thus, the nucleus has one more proton after beta decay.
An electron does not have an atomic number because it is not an atom. Most beta particles have only a single negative charge. However, scientists typically represent an electron using an atomic number of –1 in a nucleardecay equation. A beta particle’s mass is very small compared to the mass of a proton or neutron. Thus, the particle can be considered to have a mass of zero. The symbol for a negatively charged beta particle symbol is –10 e.
EHHDBG@<EHL>K "Atomic mass" of an electron "Atomic number" of an electron
0 –1
e
12. Identify What does the zero represent in the symbol for a beta particle? An electron
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What Is Radioactivity? continued
14 6
8g^i^XVaI]^c`^c\ 13. Apply Concepts Why does the mass number of an atom stay the same before and after beta decay?
C
14 7
N+
0 –1
14 = 14 + 0 6 = 7 + (–1)
e
Through the process of beta decay, a carbon-14 nucleus becomes a nitrogen-14 nucleus. The equation that describes this process is shown above. During beta decay of carbon-14, a neutron decays to form a proton and an electron. Because the nucleus gains a proton, the new isotope has a new atomic number. Thus, the new isotope is a different element.
What Happens During Gamma Decay? Recall that gamma rays are not made of particles. Thus, when an isotope emits gamma rays, the number of protons and neutrons does not change. However, the energy content of the nucleus will be lower after gamma decay. WRITING NUCLEAR DECAY EQUATIONS
Actinium-217 decays by releasing an alpha particle. Write the equation that describes this decay process, and determine which element formed. Step 1: Write the equation with the original element on the left side and the products on the right side.
12 5
B 126 C + AZ X
217 89
Ac Z X + 2 He A
4
Unknown: X = unknown decay product A = unknown mass
Math Skills 14. Write Equations Complete the following radioactive decay equation. Indicate whether alpha or beta decay takes place.
Given:
Z = unknown atomic number Step 2: Write math equations for atomic and mass numbers. Rearrange the equations.
217 = A + 4 A = 217 − 4
Step 3: Solve for the unknown values, and rewrite the equation with all nuclei represented.
A = 213 Z = 87 According to the periodic table, 87 is the atomic 213 number of francium. The unknown element is 87 Fr. 217 89
Ac
213 87
89 = Z + 2 Z = 89 − 2
4
Fr + 2 He
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What Is Radioactivity? continued
How Do Scientists Use Radioactive Decay? Scientists can use radioactive decay to determine the age of rocks and materials that were once alive. Radioactive decay can help scientists learn the ages of materials found at ancient graves and villages, and even Earth itself. It is impossible to predict the precise moment a nucleus of a single atom will decay. However, it is possible to know how long it will take for half a sample of radioactive material to decay. This is because the decay rate is the same for any sample of an isotope. The time needed for half the nuclei in a sample to decay is called the isotope’s half-life.
15. Define What is a half-life?
Half-Lives of Selected Isotopes Isotope
Half-life
Nuclear radiation emitted
Thorium- 219
1.05 × 10−6 s
α
Hafnium-156
2.5 × 10−2 s
α
Radon-222
3.82 days
α, γ
Iodine-131
8.1 days
β, γ
Radium-226
1,599 years
α, γ
Carbon-14
5,715 years
β
Plutonium-239
2.412 × 104 years
α, γ
Uranium-235 Potassium-40 Uranium-238
READING CHECK
8
α, γ
9
β, γ
9
α, γ
7.04 × 10 years 1.28 × 10 years 4.47 × 10 years
EHHDBG@<EHL>K 16. Identify Which of these radioactive isotopes has the shortest half-life? Which has the longest half-life?
Different radioactive isotopes have different half-lives. Half-lives can last from nanoseconds to billions of years. The length of a half-life depends on the stability of the nuclei of a particular isotope. An isotope’s half-life can make the isotope useful in particular situations. For example, doctors use isotopes with short half-lives, such as iodine-131, to help diagnose medical problems. Geologists calculate the ages of rocks by using the half-lives of long-lasting isotopes, such as potassium-40. USING HALF-LIFE
Radium-226 has a half-life of 1,599 years. How much time is needed for seven-eighths (7/8) of a sample of radium-226 to decay? Copyright © by Holt, Rinehart and Winston. All rights reserved.
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What Is Radioactivity? continued Step 1: List the given and unknown values.
Given: half-life = 1,599 years fraction of sample decayed = _7_ 8 Unknown: • fraction of sample remaining • total time of decay
fraction of sample remaining Step 2: Subtract the fraction decayed from 1 = 1 − fraction decayed to find how much of the = 1 − _7_ = _1_ sample remains. 8 8 Determine how much of the sample remains after each half-life.
amount of sample remaining after one half-life = _1_ 2 amount of sample remaining after two half-lives = _1_ × _1_ = _1_ 2 2 4 amount of sample remaining after three half-lives = _1_ × _1_ × _1_ = _1_ 2 2 2 8
Math Skills 17. Calculate The half-life of iodine-131 is 8.1 days. How much time is needed for three-fourths of the sample of iodine-131 to decay?
Step 3: Multiply the number of half-lives by the time needed for each half-life. This is the total time needed for _7_ of the sample to 8 decay.
Each half-life lasts 1,599 years. total time of decay 1,599 y = 3 half-lives × _______ half-life = 4,797 y
EXPONENTIAL RATE OF RADIOACTIVE DECAY
8g^i^XVaI]^c`^c\ 18. Infer As the number of carbon-14 atoms decreases over time, why does the number of nitrogen-14 atoms increase?
After the first half-life of a radioactive sample has passed, half of the sample remains unchanged. After the next half-life, half of the remaining sample decays. That is, only a quarter of the original element remains. After the next half life, only one-eighth will remain unchanged. This relationship is called an exponential decay. The original radioactive nuclei are called parent nuclei. A decay curve is a graph that shows the change in number of parent nuclei in a given sample over time. Examine the graph on the next page. The total number of nuclei remains the same, but the number of carbon nuclei decreases over time. As the number of carbon-14 atoms decrease, the number of nitrogen-14 atoms increases.
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What Is Radioactivity? continued Will the half-life ever reach zero?
3BEJPBDUJWF%FDBZPG$ 'SBDUJPOPGPSJHJOBMFMFNFOUSFNBJOJOH
Date
$BUPNT
Why or Why Not? Explain your answer.
/BUPNT
EHHDBG@<EHL>K
)BMGMJWFT
19. Predict What fraction of the original element will remain after four half-lives?
During each half-life, half of the remaining sample decays to form another element.
CARBON-14 DATING
Carbon is found in all living things. Living things may use any of the carbon isotopes in their bodies. The most common carbon isotope is carbon-12. Plants take in carbon dioxide during photosynthesis. A small fraction of the CO2 molecules they take in contain the carbon-14 isotope instead of carbon-12. While a plant or an animal that eats the plant is alive, the ratio of the carbon isotopes in its body stays about the same. When an organism dies, however, it does not take in any more carbon. The nuclei of the carbon-14 atoms decay, but those of carbon-12 do not. Scientists can compare the ratio of carbon-14 to carbon-12 to estimate how long ago an organism died. This is sometimes called carbon-14 dating. Scientists use carbon-14 dating to estimate the ages of objects made of materials that were once alive.
8g^i^XVa I]^c`^c\ 20. Infer Can scientists use carbon-dating to estimate the age of a gold ring? Explain your answer.
Scientists may use carbon-14 dating to estimate the age of a piece of ancient clothing or the age of a mummy. Copyright © by Holt, Rinehart and Winston. All rights reserved.
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Section 1 Review SECTION VOCABULARY alpha particle a positively charged particle that consists of two protons and two neutrons and that is emitted from a nucleus during radioactive decay; it is identical to the nucleus of a helium atom and has a charge of +2 beta particle an electron or positron that is emitted from a nucleus during radioactive decay gamma ray the high-energy photon emitted by a nucleus during fission and radioactive decay
half-life the time required for half of a sample of a radioactive isotope to break down by radioactive decay to form a daughter isotope nuclear radiation the particles that are released from the nucleus during radioactive decay, such as neutrons, electrons, and photons radioactive decay the disintegration of an unstable atomic nucleus into one or more different nuclides, accompanied by the emission of radiation, the nuclear capture or ejection of electrons, or fission
1. Identify Which of the four common types of nuclear radiation can be described as
an uncharged particle?
2. Explain Why are gamma rays more dangerous than alpha particles or beta
particles?
3. Describe What happens to the mass number and the atomic number of an atom
during beta decay?
4. Analyze An archaeologist finds an old piece of wood. The carbon-12 to
carbon-14 ratio is 1/16 the ratio measured in a newly fallen tree. Estimate the age of the piece of wood. (Hint: Use the table “Half-Lives of Selected Isotopes” to help you.)
5. Calculate What product is formed in the following alpha decay? Use the periodic
table in the back of the book to help you identify the element. 212 86
Rn
A Z
X + 42 He
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Nuclear Changes
SECTION
1 What Is Radioactivity?
KEY IDEAS As you read this section, keep these questions in mind:
• What is radioactivity? • What are the different types of nuclear radiation? • How does nuclear decay change an atom?
What Is Radioactivity? Our lives are affected by radioactivity, or nuclear radiation, in many ways. Technology that uses radioactivity has helped people detect disease, kill cancer cells, and generate electricity. However, too much nuclear radiation can be harmful. We need to know where radiation exists and how to protect ourselves from it. First, we need to know what radioactivity is.
READING TOOLBOX Compare As you read, make a table that compares the main types of nuclear radiation. In the table, describe their similarities and differences.
What Happens During Nuclear Decay? Recall that an element may be found in different forms called isotopes. Isotopes of an element have the same number of protons in their nuclei but different numbers of neutrons. In contrast, different elements have different numbers of protons in their nuclei. Certain isotopes of some elements go through a process called radioactive decay. During radioactive decay, an unstable atom releases energy or particles from its nucleus. Sometimes, decay must happen many times before a nucleus is stable. After radioactive decay, the element may change into a different isotope of the same element or into a completely different element. The energy and matter released by the nuclei of unstable isotopes is called nuclear radiation.
This diagram shows what happens when a particular unstable isotope emits, or gives off, nuclear radiation. This nucleus is emitting both energy and a particle.
READING CHECK 1. Describe What happens during radioactive decay?
Electron Gamma ray
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What Is Radioactivity? continued
What Are Different Types of Nuclear Radiation? There are four main types of nuclear radiation: alpha particles, beta particles, gamma rays, and neutrons. Nuclear radiation can interact with nearby matter. The charge, mass, and energy of nuclear radiation determine how it will interact with matter. Types of Nuclear Radiation Radiation type
Symbol
Mass (kg)
Charge
Alpha particle
4 2
6.646 × 10−27
+2
Beta particle
0 –1
9.109 × 10−31
−1, (+1)
none
0
1.675 × 10−27
0
He
e,
0 +1
Graphic
e
EHHDBG@<EHL>K 2. Identify Which type of radiation has the most massive particles?
Gamma ray γ
3. Identify Which two types of radiation have no charge?
Neutron
0 1
n
ALPHA PARTICLES
READING CHECK 4. Identify Which element has the same number of protons and neutrons as an alpha particle?
Ernest Rutherford discovered the alpha particle while studying the decay of uranium-238, a radioactive isotope. Rutherford named the radiation alpha (α) rays after the first letter of the Greek alphabet. Later, he discovered that alpha rays were actually particles. Alpha particles are positively charged particles made of two protons and two neutrons—the same makeup as a helium nucleus. Alpha particles do not travel far through materials. In fact, they can barely pass through a sheet of paper. Two factors limit an alpha particle’s ability to pass through materials. First, alpha particles are more massive than other types of nuclear radiation. Second, because alpha particles are charged, they remove electrons from, or ionize, matter as they pass through it. This process causes the alpha particle to lose energy and slow down.
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What Is Radioactivity? continued
BETA PARTICLES
Some decaying nuclei emit a type of nuclear radiation that travels farther through matter than alpha particles do. This nuclear radiation is made up of beta particles, which are named after the second Greek letter, beta (β). Beta particles are typically fast moving electrons. However, beta particles can also be positively charged particles called positrons. Positrons have the same mass as electrons. Scientists wondered how negatively charged beta particles could come from a positively charged nucleus. A theory introduced in the 1930s helped explain this. Recall that a neutron has no charge. Scientists found that a neutron decays to form a proton and an electron. The nucleus then ejects, or shoots out, an electron at a high speed as a beta particle. GAMMA RAYS
Unlike alpha or beta particles, gamma rays are not made of matter and do not have an electric charge. Instead, gamma rays are a form of electromagnetic energy, or light. Gamma rays are named for the third Greek letter, gamma (γ). Like visible light and X rays, gamma rays consist of energy packets called photons. Gamma rays, however, have much more energy than light or X rays do. Although gamma rays have no electric charge, they can ionize matter easily and cause damage. Clothing or most building materials cannot stop gamma rays. Thus, gamma rays are more dangerous to the health of living things than alpha or beta particles are. Alpha particles
Beta particles
READING CHECK 5. Explain How is it possible for a positively charged nucleus to release a negatively charged beta particle?
Gamma rays
EHHDBG@<EHL>K A thin sheet of paper can block alpha particles.
About 3 mm of aluminum can block beta particles.
Seven cm or more of lead are needed to block gamma rays.
6. Identify Which of the three materials shown in the figure can block alpha particles, beta particles, and gamma rays?
Different kinds of nuclear radiation can pass through, or penetrate, different materials. Copyright © by Holt, Rinehart and Winston. All rights reserved.
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What Is Radioactivity? continued
What Is Neutron Emission?
READING CHECK 7. Identify What is one cause of neutron emission?
During neutron emission, a nucleus releases neutrons. Several processes may cause neutron emission. For example, sometimes, neutrons are released when atoms are hit by large particles such as alpha particles or other neutrons. Recall that charged particles can ionize matter. Because neutrons have no charge, they do not ionize matter. Neutrons don’t lose energy ionizing matter as alpha and beta particles do. Thus, neutrons travel farther through matter than either alpha or beta particles do.
How Does Nuclear Decay Change an Atom?
READING CHECK 8. Explain Why does alpha or beta decay cause an atom to become a different element?
Nuclear decay causes changes in the nucleus of an atom. When an unstable nucleus releases an alpha or beta particle, the number of protons and neutrons changes. For instance, when radium-226 emits an alpha particle, it changes to radon-222. Nuclear decay changed the number of protons, so the atom becomes a different element. Nuclear-decay equations are written in a way similar to chemical reaction equations. The original nucleus is like a reactant, so it is placed on the left side of the equation. The products of the reaction are placed on the right side of the equation.
What Happens During Alpha Decay?
EHHDBG@<EHL>K 9. Identify What is the atomic number of radon, Rn? How many protons does an atom of radon have?
10. Identify How many neutrons are in an atom of 222 86Rn?
During alpha decay, a large unstable nucleus becomes smaller by emitting an alpha particle. Recall that an alpha particle is the same as the nucleus of a helium atom. The equation for alpha decay shows that the atomic mass decreases by four and the atomic number decreases by two. The equation that describes the alpha decay of radium-226 is shown below. 226 88
Ra
222 86
Rn + 42 He
226 = 222 + 4 88 = 86 + 2
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What Is Radioactivity? continued
MASS NUMBER AND ATOMIC NUMBER
The mass number of the radium atom before decay is 226. This number is the same as the sum of the mass numbers of the decay products. Similarly, the radium atom has 88 protons before alpha decay. This number is the same as the sum of the protons produced by the decay.
What Happens During Beta Decay? During beta decay, the mass number of an atom before and after the decay will not change. However, the atomic number after the decay increases or decreases by one. Remember that the atomic number is equal to the number of protons. Recall that the number of protons an atom has determines what element that atom belongs to. Therefore, the atom after beta decay will change to a different element. Carbon-14 nucleus
EHHDBG@<EHL>K
Nitrogen-14 nucleus Beta particle (electron)
11. Explain After beta decay, why is the atom a different element?
During beta decay, a neutron in the nucleus decays to form a proton and an electron. The electron is emitted from the nucleus, but the proton stays. Thus, the nucleus has one more proton after beta decay.
An electron does not have an atomic number because it is not an atom. Most beta particles have only a single negative charge. However, scientists typically represent an electron using an atomic number of –1 in a nucleardecay equation. A beta particle’s mass is very small compared to the mass of a proton or neutron. Thus, the particle can be considered to have a mass of zero. The symbol for a negatively charged beta particle symbol is –10 e.
EHHDBG@<EHL>K "Atomic mass" of an electron "Atomic number" of an electron
0 –1
e
12. Identify What does the zero represent in the symbol for a beta particle? An electron
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What Is Radioactivity? continued
14 6
8g^i^XVaI]^c`^c\ 13. Apply Concepts Why does the mass number of an atom stay the same before and after beta decay?
C
14 7
N+
0 –1
14 = 14 + 0 6 = 7 + (–1)
e
Through the process of beta decay, a carbon-14 nucleus becomes a nitrogen-14 nucleus. The equation that describes this process is shown above. During beta decay of carbon-14, a neutron decays to form a proton and an electron. Because the nucleus gains a proton, the new isotope has a new atomic number. Thus, the new isotope is a different element.
What Happens During Gamma Decay? Recall that gamma rays are not made of particles. Thus, when an isotope emits gamma rays, the number of protons and neutrons does not change. However, the energy content of the nucleus will be lower after gamma decay. WRITING NUCLEAR DECAY EQUATIONS
Actinium-217 decays by releasing an alpha particle. Write the equation that describes this decay process, and determine which element formed. Step 1: Write the equation with the original element on the left side and the products on the right side.
12 5
B 126 C + AZ X
217 89
Ac Z X + 2 He A
4
Unknown: X = unknown decay product A = unknown mass
Math Skills 14. Write Equations Complete the following radioactive decay equation. Indicate whether alpha or beta decay takes place.
Given:
Z = unknown atomic number Step 2: Write math equations for atomic and mass numbers. Rearrange the equations.
217 = A + 4 A = 217 − 4
Step 3: Solve for the unknown values, and rewrite the equation with all nuclei represented.
A = 213 Z = 87 According to the periodic table, 87 is the atomic 213 number of francium. The unknown element is 87 Fr. 217 89
Ac
213 87
89 = Z + 2 Z = 89 − 2
4
Fr + 2 He
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What Is Radioactivity? continued
How Do Scientists Use Radioactive Decay? Scientists can use radioactive decay to determine the age of rocks and materials that were once alive. Radioactive decay can help scientists learn the ages of materials found at ancient graves and villages, and even Earth itself. It is impossible to predict the precise moment a nucleus of a single atom will decay. However, it is possible to know how long it will take for half a sample of radioactive material to decay. This is because the decay rate is the same for any sample of an isotope. The time needed for half the nuclei in a sample to decay is called the isotope’s half-life.
15. Define What is a half-life?
Half-Lives of Selected Isotopes Isotope
Half-life
Nuclear radiation emitted
Thorium- 219
1.05 × 10−6 s
α
Hafnium-156
2.5 × 10−2 s
α
Radon-222
3.82 days
α, γ
Iodine-131
8.1 days
β, γ
Radium-226
1,599 years
α, γ
Carbon-14
5,715 years
β
Plutonium-239
2.412 × 104 years
α, γ
Uranium-235 Potassium-40 Uranium-238
READING CHECK
8
α, γ
9
β, γ
9
α, γ
7.04 × 10 years 1.28 × 10 years 4.47 × 10 years
EHHDBG@<EHL>K 16. Identify Which of these radioactive isotopes has the shortest half-life? Which has the longest half-life?
Different radioactive isotopes have different half-lives. Half-lives can last from nanoseconds to billions of years. The length of a half-life depends on the stability of the nuclei of a particular isotope. An isotope’s half-life can make the isotope useful in particular situations. For example, doctors use isotopes with short half-lives, such as iodine-131, to help diagnose medical problems. Geologists calculate the ages of rocks by using the half-lives of long-lasting isotopes, such as potassium-40. USING HALF-LIFE
Radium-226 has a half-life of 1,599 years. How much time is needed for seven-eighths (7/8) of a sample of radium-226 to decay? Copyright © by Holt, Rinehart and Winston. All rights reserved.
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Name SECTION 1
Class
Date
What Is Radioactivity? continued Step 1: List the given and unknown values.
Given: half-life = 1,599 years fraction of sample decayed = _7_ 8 Unknown: • fraction of sample remaining • total time of decay
fraction of sample remaining Step 2: Subtract the fraction decayed from 1 = 1 − fraction decayed to find how much of the = 1 − _7_ = _1_ sample remains. 8 8 Determine how much of the sample remains after each half-life.
amount of sample remaining after one half-life = _1_ 2 amount of sample remaining after two half-lives = _1_ × _1_ = _1_ 2 2 4 amount of sample remaining after three half-lives = _1_ × _1_ × _1_ = _1_ 2 2 2 8
Math Skills 17. Calculate The half-life of iodine-131 is 8.1 days. How much time is needed for three-fourths of the sample of iodine-131 to decay?
Step 3: Multiply the number of half-lives by the time needed for each half-life. This is the total time needed for _7_ of the sample to 8 decay.
Each half-life lasts 1,599 years. total time of decay 1,599 y = 3 half-lives × _______ half-life = 4,797 y
EXPONENTIAL RATE OF RADIOACTIVE DECAY
8g^i^XVaI]^c`^c\ 18. Infer As the number of carbon-14 atoms decreases over time, why does the number of nitrogen-14 atoms increase?
After the first half-life of a radioactive sample has passed, half of the sample remains unchanged. After the next half-life, half of the remaining sample decays. That is, only a quarter of the original element remains. After the next half life, only one-eighth will remain unchanged. This relationship is called an exponential decay. The original radioactive nuclei are called parent nuclei. A decay curve is a graph that shows the change in number of parent nuclei in a given sample over time. Examine the graph on the next page. The total number of nuclei remains the same, but the number of carbon nuclei decreases over time. As the number of carbon-14 atoms decrease, the number of nitrogen-14 atoms increases.
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Name
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SECTION 1
What Is Radioactivity? continued Will the half-life ever reach zero?
3BEJPBDUJWF%FDBZPG$ 'SBDUJPOPGPSJHJOBMFMFNFOUSFNBJOJOH
Date
$BUPNT
Why or Why Not? Explain your answer.
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EHHDBG@<EHL>K
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19. Predict What fraction of the original element will remain after four half-lives?
During each half-life, half of the remaining sample decays to form another element.
CARBON-14 DATING
Carbon is found in all living things. Living things may use any of the carbon isotopes in their bodies. The most common carbon isotope is carbon-12. Plants take in carbon dioxide during photosynthesis. A small fraction of the CO2 molecules they take in contain the carbon-14 isotope instead of carbon-12. While a plant or an animal that eats the plant is alive, the ratio of the carbon isotopes in its body stays about the same. When an organism dies, however, it does not take in any more carbon. The nuclei of the carbon-14 atoms decay, but those of carbon-12 do not. Scientists can compare the ratio of carbon-14 to carbon-12 to estimate how long ago an organism died. This is sometimes called carbon-14 dating. Scientists use carbon-14 dating to estimate the ages of objects made of materials that were once alive.
8g^i^XVa I]^c`^c\ 20. Infer Can scientists use carbon-dating to estimate the age of a gold ring? Explain your answer.
Scientists may use carbon-14 dating to estimate the age of a piece of ancient clothing or the age of a mummy. Copyright © by Holt, Rinehart and Winston. All rights reserved.
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Section 1 Review SECTION VOCABULARY alpha particle a positively charged particle that consists of two protons and two neutrons and that is emitted from a nucleus during radioactive decay; it is identical to the nucleus of a helium atom and has a charge of +2 beta particle an electron or positron that is emitted from a nucleus during radioactive decay gamma ray the high-energy photon emitted by a nucleus during fission and radioactive decay
half-life the time required for half of a sample of a radioactive isotope to break down by radioactive decay to form a daughter isotope nuclear radiation the particles that are released from the nucleus during radioactive decay, such as neutrons, electrons, and photons radioactive decay the disintegration of an unstable atomic nucleus into one or more different nuclides, accompanied by the emission of radiation, the nuclear capture or ejection of electrons, or fission
1. Identify Which of the four common types of nuclear radiation can be described as
an uncharged particle?
2. Explain Why are gamma rays more dangerous than alpha particles or beta
particles?
3. Describe What happens to the mass number and the atomic number of an atom
during beta decay?
4. Analyze An archaeologist finds an old piece of wood. The carbon-12 to
carbon-14 ratio is 1/16 the ratio measured in a newly fallen tree. Estimate the age of the piece of wood. (Hint: Use the table “Half-Lives of Selected Isotopes” to help you.)
5. Calculate What product is formed in the following alpha decay? Use the periodic
table in the back of the book to help you identify the element. 212 86
Rn
A Z
X + 42 He
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