Kelter P., Mosher M., Scott A. Chemistry. The Practical Science

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128

130

132

134

136

138

140

142

144

0.71 Gy

25 h

19 d

11 d

3.9 s

0.1 ms

0.5 s

4.8

min

36 min

2.13 min

32 ky

22 y

235

231

227

223

219

215

211

207

211

215

219

223

227

231

126

81 82 83 84 85 86 87 88 89 90 91 92 93 94

Number of neutrons

Atomic number

The Uranium-235 Decay Series

778 µs

128

130

132

134

136

138

140

142

144

232

228

212

216

224

220

216

212

208

228

14 Gy

6.7 y

6.1 h

1.9 y

3.7 d

55 s

11 h

164 µs

0.3 µs

3.1

min

126

81 82 83 84 85 86 87 88 89 90 91 92 93 94

Atomic number

The Thorium-232 Decay Series

128

130

132

134

136

138

140

142

144

238

234

230

226

222

218

214

210

218

214

210

234

206

4.5 Gy

25 d

6.7 h

0.23 My

83 ky

1.6 ky

3.8 d

150 µs

22 y

140 d

1281.3

min

4.2

min

27 min

126

81 82 83 84 85 86 87 88 89 90 91 92 93 94

Number of neutrons

Atomic number

The Uranium-238 Decay Series

206

3.1 min

128

130

132

134

136

138

140

142

144

209

225

209

213

217

221

225

229

223

237

233

47 min

4.2 ms

20 ms

4.8 min

10 d

7 ky

15 d

0.16 My

2.3 My

27 d

126

81 82 83 84 85 86 87 88 89 90 91 92 93 94

Atomic number

The Neptunium-237 Decay Series

908 Chapter 21 Nuclear Chemistry

FIGURE 21.4

The four natural decay

series. Each decay series

begins at the nuclide

listed at the top right-

hand side of the series

and proceeds to the

lower left-hand side

by nuclear decay. The

half-life of many

of these transitions

are indicated in red

numbers. Gamma

emissions accom-

pany many of these

decays.

21.3 Interaction of Radiation with Matter 909

decrease Z by 2, thus moving the line to the left. But a beta-minus emission in-

creases Z by 1 unit. If beta emission follows an alpha emission, there is a zag back

to the right. The series that begins with

235

U ends with the stable lead-207 iso-

tope, and the

238

U series forms

206

Pb. There are two other naturally occurring

decay series, one that begins with

237

Np to form

209

Bi, and one in which

232

decays to ultimately form

208

Pb.Along the way, these decay chains provide dozens

of radioisotopes that we typically ﬁnd in our biosphere. This is one of the

sources of naturally occurring radioactive isotopes. Of particular concern is

radon, a radioactive gas that can collect in basements dug into soil that is rich in

uranium ores. Is radon harmful to humans? Understanding the relationship

between radioactivity and human health will help us answer this question.

HERE’S WHAT WE KNOW SO FAR

■

Radioactivity results from the decay of an unstable nucleus.

■

There are three main types of radioactive decay and three common forms of

radioactivity.

■

The alpha particle is a fast-moving helium nucleus.

■

The beta particle is an electron ejected from the nucleus of an unstable atom.

■

The gamma ray is a burst of high-energy electromagnetic radiation.

■

A decay series is a stepwise progression of a radioactive nuclide toward

stability.

21.3

Interaction of Radiation with Matter

Taking a walk on a crisp, sunny day is one of the pleasures of autumn. Any cloud

that blocks the Sun is easily noticed. Not only does the shade reduce the amount

of light hitting your eyes, but your skin also registers the change. The energy ex-

changes, from the infrared through the ultraviolet regions of the electromagnetic

spectrum, are apparent and profound. However, when it comes to detecting the

small amounts of alpha particles, beta particles, and gamma rays that bombard

you on a daily basis, your senses don’t help. For instance, you cannot detect the

alpha particles that radioactive radon, an odorless, colorless, and tasteless gas,

emits.

Though seemingly invisible, the different types of radiation form quite a nu-

clear arsenal, as summarized in Figure 21.5. We can envision alpha particles as the

cannon balls of the group. With their greater size and +2 charge, they do not

travel very far before they smash into other atoms. The typical collision results

in the capture of two electrons to form a neutral helium atom. In contrast, beta

particles, being smaller and traveling more rapidly, are the equivalent of high-

velocity bullets. They are able to travel signiﬁcantly longer distances before a

collision, but they lack the punch of an alpha particle. Gamma rays, with no

mass and no charge, are akin to laser weapons. They shoot great distances

through matter, now and then searing something in their path. What about the

Application

Tissue

Aluminum Concrete Lead

FIGURE 21.5

Alpha, beta, and gamma radiation differ

in their penetration. Gamma rays are

the most highly penetrating, and alpha

particles the least.

Molecule

Collision of an alpha particle and a

molecule results in the formation of an

atom of helium.

Application

Water (neutral) Water (cation radical)

antineutrinos that accompany beta emissions? Having neither a mass nor a

charge, they are not absorbed and are considered harmless.

The type and the energy of the radiation dictate what must be used to shield

us to the greatest extent possible (see Table 21.3). Alpha particles penetrate mat-

ter the least, being stopped by just a few centimeters of air, by the outer layer of

your skin (which is mostly dead cells), or by a piece of paper. Beta particles pen-

etrate more deeply and can pass through several pieces of paper, through a thin

sheet of aluminum, or about a centimeter into your skin. In contrast, gamma rays

can pass right through you. Shielding your body from them requires several

inches of aluminum or lead, and even these may not do the job.

A visit to the dentist reveals an interesting feature of stopping damage from

nuclear radiation. Before an X-ray of a patient’s teeth is obtained, the patient is

typically draped with a sheet of lead. Why is lead one of the materials employed

to shield us from high-energy electromagentic radiation, such as X-rays or nu-

clear radiation? The high density of lead, 11.3g/cm

, means that only two inches

of lead will easily shield you from alpha and beta radiation, as well as from most

gamma radiation. However, lead is not unique in this ability. Gold (d =

19.3 g/cm

) is more dense than lead and would work even better. Bricks or blocks

of a moderately dense material such as concrete also would do the trick. However,

no dentist is likely to place an apron of gold or a foot of concrete over your ab-

domen before taking dental X-rays. Given its density and price, lead is often the

shielding medium of choice.

Although alpha, beta, and gamma radiation differ in penetration, they are

alike in the effects they produce on the molecular level.All three are known as

ion-

izing radiation

; that is, they are capable of forming ions by knocking electrons out

of atoms. The damage they cause is the reason for their detection with, for exam-

ple, a Geiger counter or ﬁlm badge.

The consequences of ionizing radiation can be negligible or severe, depend-

ing on how many molecules are damaged inside the body. Although small

amounts of radiation typically lead to only negligible damage that can be

repaired by the body, large doses of radiation can be life-threatening.

How does

ionizing radiation cause damage?

Because between about 50% and 70% of your

body is water, a scenario of particular interest occurs when ionizing radiation

strikes a water molecule. The blow can knock off an electron to form a highly re-

active species with an unpaired electron:

O e





ionizing

radiation



910 Chapter 21 Nuclear Chemistry

Differences in Penetration and Shielding for Different Types of Radiation

Penetration Penetration in

Type Examples in Dry Air Skin or Tissue

†

Shielded by Q*

Alpha uranium, plutonium, 2–4 cm 0.05 mm Paper, air, clothing 20

americium

Beta potassium-40, cesium-137 200–300 cm 4–5 mm Heavy clothing ~1

Gamma technetium, cobalt-60 500 m 50 cm Lead, concrete ~1

Fast neutrons Accelerators Several hundred feet High Water, plastic concrete 20

TABLE 21.3

*Q is the relative biological effectiveness, a factor that indicates relative amounts of damage to living tissue.

†

Alpha, beta, and gamma radiation all exhibit a range of energies. The degree of penetration depends on the actual energy.

Use of radiation shield on a patient at

the dentist’s ofﬁce.

Application

HEMICAL ENCOUNTERS:

Radiation and Cancer

Electron density maps of water and the radical

cation of water. Note the decrease in electron

density around the oxygen end of the molecule.

The resulting radical cation (see Chapter 7) undergoes autoprotolysis to form

hydroxyl free radicals:

O·



+ H



+ ·OH

The fate of the hydroxyl free radicals is particularly damaging to the cells within

your body. If they encounter a molecule of DNA in a dividing cell, they may

damage a section of the genetic code (Figure 21.6). The damage could result in

death of the cell, triggering the formation of mutant proteins (proteins with a

non-natural primary structure; see Chapter 22) or triggering an abnormal func-

tion of the cell leading to cancer. In short, nuclear radiation can be carcinogenic.

Although we do not know exactly what cellular events ensue after a dose of ion-

izing radiation, two things seem clear: (1) The more radiation a person is exposed

to, the greater the likelihood of that person’s developing cancer. (2) These cancers

may not show up until decades after the time of exposure.

Is there a threshold below which radiation is safe? Recent studies have convinc-

ingly demonstrated that the damage inﬂicted by low-level radiation upon workers

in the nuclear industry and upon World War II nuclear bomb survivors have been

greatly underestimated. Similarly, the link between fetal X-rays (an abandoned

medical practice) and childhood cancer has been established. Fortunately,because

cancer cells grow and divide, they also are susceptible to radiation. Carefully mea-

sured doses of radiation directed at cancerous cells can result in their death.

Overall, the biological effects of nuclear radiation depend on the quantity of

energy transferred to the cells and tissues. In the United States, the

rem or “roent-

gen equivalent in man” is the unit for estimating the damage. Other units that

measure radiation include the

becquerel, curie, roentgen, and rad. Of these, only

the becquerel (Bq) is an SI unit. Scientists in most parts of the world employ two

other SI units, the

sievert (Sv) and the gray (Gy), which are related to the rem and

the rad, respectively, as shown in Table 21.4.

21.3 Interaction of Radiation with Matter 911

Base

damage

Single-strand

break

Double-strand

break

Double-strand

breaks

FIGURE 21.6

Examples of chromosomal damage from

radiation.





Units for Measuring Radiation

Measure of Name Abbreviation Deﬁnition

Activity becquerel* Bq 1 disintegration per second

Activity curie Ci 1 curie = 3.7 × 10

becquerel

Exposure roentgen R 1 roentgen = 2.58 × 10

−4

couloumbs of

charge per kg of air

Absorbed dose radiation absorbed rad 1 rad =1 × 10

−2

J of energy deposited

dose per kg of tissue

Absorbed dose gray* Gy 1 gray = 100 rad

Dose equivalent roentgen equivalent rem Q × absorbed dose

in man

Dose equivalent sievert* Sv 1 sievert = 100 rem

*SI units

TABLE 21.4

The quantity of energy absorbed by tissues is directly related to the time of

exposure to ionizing radiation. In fact, time is an important part of the decision-

making process in medical diagnosis and treatment. For example, prostate cancer in

elderly men is often treated by the implantation of metal “seeds” coated with

125

or, more recently,

103

Pd. Why use these nuclides? They are sufﬁciently radioactive

for only the time needed to control the cancer without creating new cancers.

How

do we know how long they will be radioactive?

The most important measure that

we use to judge the length of time a substance is radioactive is its half-life.

The U.S. Environmental Protection Agency suggests that the average person

receives an annual dose of 0.3 rem of radiation from natural sources. Over the

course of a lifetime, this is predicted to result in 5 or 6 deaths due to cancer per

10,000 people. This sounds shocking until we consider that the rate of deaths due

to cancer from nonradioactive sources is predicted to be about 2000 people per

10,000. Larger doses received in one exposure have a much more deleterious

effect on human health, as shown in Table 21.5. Acute exposures, such as those

that result from accidents in nuclear power plants and those that resulted from

the U.S. bombing of Japan in World War II, cause severe damage to the human

body, often resulting in lifelong health problems and even death.

21.4 The Kinetics of Radioactive Decay

The half-life, t

1/2

, of a radioactive isotope is the period of time it takes for exactly

half of the original nuclei in a radioactive sample to decay. We discussed half-life

in detail in Chapter 15. Table 21.6 shows that half-lives can vary widely among

the radioactive isotopes. They can be as short as a few microseconds and

as long as a few billion years.

How can the half-life tell us how much radioactivity remains after a

given time? Remember from Chapter 15 that after one half-life, one-half

of the sample has reacted and only one-half of the sample remains. After

a second half-life,

⁄

4 of the sample is left. After 3 half-lives,

⁄

2 of

⁄

2,or (

⁄

8, of the sample remains. More generally, then, for n half-

lives, the fraction of the original sample remaining is (

⁄

. This trend is

shown in Figure 21.7 and is valid for all radioactive decay processes.

Palladium-103, used to coat the seeds implanted in the prostate, de-

cays by electron capture, in which an inner-orbital electron is captured

by a proton in the nucleus to form a neutron. The half-life of Pd-103 is

16.97 days. How long will it take for the radiation to be diminished to

1.00% of its original value so it is considered safe for radiation workers,

the prostate cancer patient, and his family? A look at Figure 21.7 indi-

cates that this will take between 6 and 7 half-lives, or between 102 and

912 Chapter 21 Nuclear Chemistry

Health Effects of Acute Radiation Exposure

Exposure (rem) Health Effect Time to Onset

10 Burns, changes in blood chemistry

50 Nausea Hours

75 Vomiting, hair loss 2–3 weeks

100 Hemorrhage

400 Death Within 2 months

1000 Internal bleeding, death Within 1–2 weeks

2000 Death Within hours

TABLE 21.5

Half-lives of Some

Radioactive Elements

Element Nuclide Half-life

nobelium

250

No 250 s

technetium

99m

Tc 6.0 h

thallium

201

Tl 21.5 h

radon

222

Rn 3.8 d

iodine

131

I 8.040 d

palladium

103

Pd 16.97 d

cobalt

Co 5.271 y

hydrogen

H 12.3 y

carbon

C 5730 y

radium

226

Ra 1.6 × 10

uranium

238

U 4.5 × 10

TABLE 21.6

119 days. Such approximations are often sufﬁcient. When necessary, we can also

solve explicitly for n.

(

⁄2)

= 1/100 = 0.0100

Taking the natural logarithm (ln) of both sides yields

n[ln(

⁄2)] = ln(0.0100)

n(−0.693) =−4.605

n = 6.645 half-lives

Solving for the time needed, we ﬁnd that

t = 6.645 half-lives × 16.97 days/half-life

= 113 days

There is another approach based on the understanding that radioactive iso-

topes decay via ﬁrst-order kinetics. Recall from Chapter 15 that the relationship

among concentration, time, and half-life for any ﬁrst-order process is shown by

]

=−kt

where A

= the amount of substance remaining

= the initial amount of substance

= the ﬁrst-order rate constant for the reaction (in this case, the decay)

t = time

We also know that the rate constant for a ﬁrst-order reaction can be determined by

k =

0.693

1/2

This means that we can solve explicitly for the rate constant if we are given the

half-life, t

1/2

. In our example,

k =

0.693

1/2

0.693

16.97 day

= 0.04084 day

−1

Assuming that we start with A

= 1.000, we can determine that if we only have 1%

remaining, A

= 0.0100. Then

[0.0100]

[1.00]

=−0.04084t

−4.605 =−0.04084t

113 = t

so t = 113 days, and we obtain the same answer (113 days) by either method.

21.4 The Kinetics of Radioactive Decay 913

2000

4000

6000

8000

10,000

12,000

01234567891011

Number of half-lives

Number of radon atoms

FIGURE 21.7

The kinetics of radioactive decay. The half-life

of a radioisotope, such as radon, is the time

required for half of the nuclei in the radio-

active sample to decompose.

Three palladium-103 “seeds,”

which are used for the treatment

of prostate cancer, easily ﬁt on

the top of a penny.

Visualization: Half-Life of Nuclear

Decay

Video Lesson: Rates of

Disintegration Reactions

But when would the entire Pd-103 sample be gone? This is a question we

cannot precisely answer, although we can come very close. Why are we unable to

tell when all of the Pd-103 is gone? After each half-life, half of the number of

radioactive atoms remaining from a previous half-life are still remaining. Sooner

or later, after a very large number (roughly 80) of half-lives have passed, only two

radioactive atoms remain for every mole we started with. Half-life is a statistical

measure. Probabilities, which don’t apply with a sample size of two, will not

accurately tell the rate of the reaction.

EXERCISE 21.4 Half-life Calculations: Here Today, Gone Tomorrow?

After exercising on a treadmill, a patient was given thallium-201 for a diagnostic

scan of his heart (Figure 21.8). How long will it take for 95.0% of the thallium to

have decayed? The half-life of thallium-201 is 21.5 hours.

Solution

As discussed previously, we can solve the problem in two ways. Using the ﬁrst

method, we ﬁnd the number of half-lives that pass until 5.0%, or a fraction of 0.050,

of the Tl-201 remains.

(

⁄2)

= 0.050

n[ln(

⁄2)] = ln(0.050)

n(–0.693) = –3.00

n = 4.32 half-lives

t = 4.32 half-lives × 21.5 hours/half-life = 93 hours

Using the second method, we proceed as follows:

k =

0.693

1/2

0.693

21.5h

= 0.0322 h

−1

[0.050]

[1.00]

=−0.0322t

−3.00 =−0.0322t

93 hours = t

PRACTICE 21.4

The half-life of

198

Au is 2.69 days. How long would it take for 99% of a gold-198

sample to decay?

See Problems 39–42 and 47–48.

The previous problem involved percentages. But you also can work half-life

problems given a starting mass or a starting number of atoms. Both are measures

of the radioactivity present. Similarly, you can work half-life problems given a

unit of activity such as the number of disintegrations per second (becquerels) or

curies, because these also measure the amount of radioactivity and are propor-

tional both to the mass and to the number of atoms. Such variations in units re-

ﬂect the differing needs of real-world situations where you are likely to encounter

radioisotopes.

The half-life of a radioactive isotope can also help you to determine how

long the radioisotope will be useful or, perhaps, to weigh the hazards associated

with that particular isotope. For example, would you rather be around a

radioisotope that decayed to 1% of its activity in 10 seconds or one that did so in

10 centuries? For the latter, the rate of decay is much lower, and you would be

914 Chapter 21 Nuclear Chemistry

FIGURE 21.8

Proton

Neutron

bombarded with far fewer alpha particles, beta particles, or gamma rays in a given

time period. This principle is important in the use of technetium in medical

imaging. We have noted that technetium-99m is a gamma emitter. It has a half-

life of 6.01 hours, which is long enough for a medical procedure, but short

enough that the substance doesn’t persist very long.

99m

Tc →

Tc +

 t

1/2

= 6.01 h

The product nuclide,

, is still radioactive. However, with its half-life of

213,000 years, the activity of Tc-99 as a beta emitter is low. In the two and a half

weeks it takes for the majority of Tc-99 to be completely eliminated from the

body, it does little damage.

21.5

Mass and Binding Energy

By now you might be a bit suspicious. Many nuclei are unstable and sponta-

neously decay. Signiﬁcant amounts of energy are released during alpha, beta,

and gamma emission—enough to ionize molecules or to kill cancer cells—but we

haven’t talked about the source of the energy.

Where does it come from, and how

does this help explain the decay processes that nuclei undergo?

The place to start to ﬁnd an answer is with Einstein’s famous equation,

E = mc

in which the constant, c, is equal to the speed of light. This relationship illustrates

that a particular mass, when completely converted, is equivalent to a surprisingly

large quantity of energy. Any chemical reaction that is accompanied by a loss in

energy, such as in an exothermic reaction, actually also has a corresponding loss

in mass. However, the mass losses are so minuscule that we cannot detect them

using conventional instruments. In contrast, the changes in mass due to a nuclear

reaction, though tiny, are quite measurable.

Let’s explore this connection by examining the formation of nitrogen-14

from its individual nuclear particles:

7p +7n →

N nucleus

A mole of nitrogen-14 nuclei (without any electrons) weighs 13.99540 g. What is

the mass of 7 separate moles of protons (1.00727 g/mol) and 7 mol of neutrons

(1.008665 g/mol)?

7 mol of protons × 1.00727 g/mol = 7.05089 g

7 mol of neutrons × 1.008665 g/mol = 7.060655 g

Total mass = 7.05089 g + 7.060655 g = 14.11154 g

This exceeds the mass of a mole of nitrogen-14 nuclei by (14.11154 g−13.99540 g) =

0.11614 g. This

mass defect, the mass difference between the individual protons

and neutrons and the composite nucleus, was used in binding the protons and

neutrons together within the nucleus. The

binding energy, expressed as a positive

number, is the energy required to dismantle the nucleus into its individual pro-

tons and neutrons. To ensure that our calculations give us positive numbers for

binding energy, we typically use Einstein’s equation in a different form:

∆E = |∆m|c

where ∆E is the binding energy and |∆m| is the absolute value of the change in

mass in kilograms. We use kilograms because our SI unit of energy, the joule,

is deﬁned as kg·m/s

. For nitrogen-14, using our mass defect of 0.11614 g

(= 1.1614

−

kg), the binding energy can be calculated as

∆E = |∆m|c

= |–1.1614

−

kg|

(2.9979

m/s)

= 1.04

21.5 Mass and Binding Energy 915

Seven protons and seven neutrons form

the nucleus of nitrogen-14.

Video Lesson: Binding Energy

EXERCISE 21.5 The Energy Advantage of Nuclear Reactions

When bombarded with neutrons, uranium-235 can split to form bromine-87,

lanthanum-146, and three neutrons. The masses reported here are those of the bare

nuclei.

235

U +

n →

Br +

146

La + 3

grams/mole 234.9936 1.008665 86.90156 145.8944 3.0260

Calculate the mass defect and the energy released in kJ/mol.

Solution

The mass defect is the difference in mass between the ending and starting materials.

∆m = (86.90156 + 145.8944 + 3.0260) − (234.9936 + 1.008665)

=−0.1803 g/mol =−1.803

−4

kg/mol

The energy equivalent to this mass is ∆E = |∆m|c

∆E = |∆m|c

= |–1.803

−4

kg/mol |

(2.9979

m/s)

= 1.621

J/mol = 1.621

kJ/mol

This is many orders of magnitude greater than the energy released by an equivalent

mass of materials in a combustion reaction.

Even though this problem uses the masses of the bare nuclei, the problem could

have been solved using the atomic masses, because the number of electrons on each

side of the equation remains constant. In radioactive decay processes that involve a

change in the number of protons, the mass of the electrons must also be considered

in the calculation of the mass defect, when atomic masses are used.

PRACTICE 21.5

Calculate the energy released in the following process.

224

Ra →

220

Rn +

See Problems 53 and 54.

Some atoms are more thermodynamically stable than others. A table of

binding energies shows only that the values generally increase as the atoms get

heavier. However, if you recalculate the binding energy for each atom and report

the values per nucleon (proton or neutron), the stabilities pop right out at you.

Nuclei with greater binding energies per nucleon are more stable. Note in Fig-

ure 21.9 that the lightest elements, those with mass numbers of 20 or less, have

the lowest binding energies per nucleon. In comparison with iron, helium simply

does not have enough nucleons to be as strongly glued together. The process that

liberates energy on the sun,

fusion (or nuclear fusion), is energetically favorable

because lighter elements such as helium are joined to form heavier ones that have

a more favorable binding energy per nucleon.

916 Chapter 21 Nuclear Chemistry

Deuteron

Energetic

neutron

Triton Helium

nucleus

Fusion

reaction

Nuclear fusion.

Visualization: Nuclear Fusion

Video Lesson: Nuclear Fusion

The heaviest elements also have somewhat lower stability. Ura-

nium, with so many protons and neutrons packed into its nucleus,

has a lower binding energy per nucleon than iron or cobalt. As we

will see in Section 21.7, it is energetically favorable to split heavier

nuclei into smaller ones via

ﬁssion (or nuclear ﬁssion) to form nuclei

with a more favorable binding energy per nucleon.

Finally, look at the maximum of the curve and you will ﬁnd

elements with the most stable nuclei—those with mass numbers

around 60, such as iron and nickel. Other elements also have sur-

prisingly high binding energies given their mass number, such as

He (an alpha particle),

C, and

O. Alternatively, one might argue

that the values for

Li and

N are surprisingly low.

21.6

Nuclear Stability and

Human-made Radioactive Nuclides

“Here today, gone tomorrow” doesn’t apply to most of the atoms that make up

our world. That is fortunate for us. In fact, the majority of the atoms on our

planet that are here today can be expected to be here tomorrow. Although it may

be hard to locate a speciﬁc atom from one day to the next, you can be reasonably

sure that it is still here. Why? Most atoms on Earth are not radioactive.

Which factors seem to affect nuclear stability? Measurements indicate that

nature favors even numbers of protons. Elements such as helium, oxygen, iron,

and lead that have even atomic numbers tend to be more abundant than their

odd neighbors. For example, of the eight elements that make up over 99% of

Earth’s total mass, only one (aluminum) has an odd atomic number. Still more

favored are nuclei that have even numbers of both protons and neutrons. Perhaps

the most dramatic case is

He, the alpha particle. Given this stability, it is not sur-

prising that helium is the second most abundant element in the universe.

Experimental data conﬁrm that certain numbers of either protons or neu-

trons (called “magic numbers”) are favored: 2, 8, 20, 28, 50, 82, and 114. The ele-

ments helium (Z

=2), oxygen (Z =8), calcium (Z = 20), and nickel (Z = 28) have

21.6 Nuclear Stability and Human-made Radioactive Nuclides 917

Two neutrons

from fission

Nucleus

Neutron

Nuclear ﬁssion.

Oxygen (shown here in liquid form), cal-

cium, and nickel have magic numbers of

nucleons.

0 20 40 60 80 100 120 140 160 180 200 220 240

235

Average binding energy per nucleon (MeV)

Number of nucleons in nucleus, A

FIGURE 21.9

The binding energy per nucleon reaches a

maximum near iron, atomic number 26.

Visualization: Nuclear Fission

Video Lesson: Nuclear Fission