Chapter 31

Nuclear Physics and Radioactivity

AP Learning ObjectivesNuclear Physics Nuclear reactions (including conservation of mass

number and charge) Students should understand the significance of the

mass number and charge of nuclei, so they can: Interpret symbols for nuclei that indicate these

quantities. Use conservation of mass number and charge to

complete nuclear reactions. Determine the mass number and charge of a

nucleus after it has undergone specified decay processes.

Students should know the nature of the nuclear force, so they can compare its strength and range with those of the electromagnetic force.

Students should understand nuclear fission, so they can describe a typical neutron-induced fission and explain why a chain reaction is possible.

AP Learning ObjectivesNuclear Physics Mass-energy equivalence

Students should understand the relationship between mass and energy (mass-energy equivalence), so they can: Qualitatively relate the energy released in

nuclear processes to the change in mass. Apply the relationship E = (m)c2 in

analyzing nuclear processes.

Table Of Contents

1. Nuclear Structure

2. The Strong Nuclear Force and The Stability of the Nucleus

3. The Mass Defect of the Nucleus and Nuclear Binding Energy

4. Radioactivity

5. The Neutrino

6. Radioactive Decay and Activity

7. Radioactive Dating

8. Radioactive Decay Series

9. Radiation Detectors

Chapter 31:Nuclear Physics and Radioactivity

Section 1:

Nuclear Structure

The atomic nucleus consists of positively charged protons and neutral neutrons.

Nuclear Structure

neutrons

ofNumber protons

ofNumber neutrons and

protons ofNumber

NZA

atomicnumber

massnumber

Identifying Variables

Isotopes Nuclei can contain the same number of protons but

a different number of neutrons isotopes.

3115 m102.1 Ar

Approximate size of a Nucleus

massnumber

3115 m102.1 Ar

Conceptual Example 1 Nuclear Density

It is well known that lead and oxygen contain different atoms andthat the density of solid lead is much greater than gaseous oxygen.Using the equation, decide whether the density of the nucleus in alead atom is greater than, approximately equal to, or less than thatin an oxygen atom.

33115102.134 Am

Am

V

M

Nuclear density are always “the same”

31.1.1. What is the primary difference between 13C and 12C?

a) The number of electrons is different.

b) The number of protons is different.

c) The number of neutrons is different.

d) The chemical behavior is different.

e) Only 12C is true carbon. The other is called carbomite.

31.1.2. How many neutrons and how many protons are in ?

a) 22 neutrons and 10 protons

b) 12 neutrons and 10 protons

c) 10 neutrons and 12 protons

d) 10 neutrons and 22 protons

e) 10 neutrons and 10 protons

Ne2210

31.1.3. Which of the following statements best describes the difference between an element and an isotope?

a) An isotope has a particular number of protons and neutrons, while an element has a particular number of protons and a varying number of neutrons.

b) An element has a particular number of protons and neutrons, while an isotope has a particular number of protons and a varying number of neutrons.

c) Chemists speak in terms of elements, while physicists prefer the more specific term of isotope.

d) An isotope has a particular number of protons and neutrons, while an element has a particular number of neutrons and a varying number of protons.

e) An element has a particular number of protons and neutrons, while an isotope has a particular number of neutrons and a varying number of protons.

31.1.4. Which one of the following elements do you think has the nucleus with the largest volume?

a) Helium (He)

b) Lithium (Li)

c) Oxygen (O)

d) Calcium (Ca)

e) Boron (B)

31.1.5. Consider the nucleus Which one of the following statements is true?

a) This isotope contains an equal number of protons and neutrons.

b) This isotope contains 91 neutrons and 143 protons.

c) This isotope contains 143 neutrons and 91 protons.

d) This isotope contains 234 neutrons and 91 protons.

e) This isotope contains 91 neutrons and 234 protons.

Pa.23491

31.1.6. What is the difference between the atomic number and the atomic mass number?

a) The atomic number is the number of protons, but the mass number is the number of neutrons.

b) The mass number is the atomic number plus the number of neutrons.

c) The mass number is the atomic number plus the number of electrons.

d) The atomic number and mass number are not related in any way.

e) The mass number and the atomic number are exactly the same thing.

Chapter 31:Nuclear Physics and Radioactivity

Section 2:The Strong Nuclear Force & The Stability of the Nucleus

What Holds a Nucleus Together?

The mutual repulsion of the protons due to the

Electric Force should push the nucleus apart.

What then, holds the nucleus together?

A stronger force within the Nucleus

What do Physicist creatively call this force?

The strong nuclear force.

Stability of the Nucleus

As nuclei get larger,

more neutrons are

required for stability.

The neutrons act like

glue without adding

more repulsive force.

For “small” elements

Ratio N/P ~ 1

For “large” element

Ratio of N/P ~ 2

31.2.1. Consider the following three forces: gravity, electromagnetic, and strong nuclear. Which of these is responsible for holding nuclei together and which is responsible for holding electrons in their orbits?

a) Gravity holds electrons, while the strong nuclear force holds nuclei together.

b) Gravity holds electrons in their orbits and nuclei together.

c) Gravity holds electrons, while the electromagnetic force holds nuclei together.

d) The strong nuclear force holds electrons, while the electromagnetic force holds nuclei together.

e) The electromagnetic force holds electrons, while the strong nuclear force holds nuclei together.

Chapter 31:Nuclear Physics and Radioactivity

Section 3:The Mass Defect of the Nucleus & Nuclear Binding Energy

22deficit Massenergy Binding cmc

Mass Deficit

Example 3 The Binding Energy of the Helium Nucleus Revisited

The atomic mass of helium is 4.0026u and the atomic mass of hydrogenis 1.0078u. Using atomic mass units, instead of kilograms, obtain thebinding energy of the helium nucleus.

u 0304.0u 0026.4u 0330.4 m

MeV 5.931u 1

MeV 3.28energy Binding

Binding Energy

31.3.1. Consider the plot of binding energy per nucleon versus the nucleon number A. Which one of the following statements best describes the stability of the iron isotope ?

a) This isotope has the most stable nucleus because a minimum amount of work is needed to separate this nucleus into its constituent protons and neutrons.

b) This isotope has the most stable nucleus because a maximum amount of work is needed to separate this nucleus into its constituent protons and neutrons.

c) This isotope has the least stable nucleus because a minimum amount of work is needed to separate this nucleus into its constituent protons and neutrons.

d) This isotope has the least stable nucleus because a maximum amount of work is needed to separate this nucleus into its constituent protons and neutrons.

e) This isotope has the most stable nucleus because an infinite amount of work is needed to separate this nucleus into its constituent protons and neutrons.

Fe5626

31.3.2. Consider the following values for the mass defect for five hypothetical nuclei labeled with roman numerals in the table below. Which one of the following statements concerning these nuclei is true?

a) Nucleus V is the most stable; and nucleus I is the least stable.

b) Nuclei I and II are the most stable; and nuclei IV and V are not stable.

c) Nuclei I and II are not stable; and nuclei IV and V are the most stable.

d) Nucleus III is the most stable; and nuclei I and V are the least stable.

e) Nucleus III is the most stable; and nuclei IV and V are the least stable.

Chapter 31:Nuclear Physics and Radioactivity

Section 4:Radioactivity

A magnetic field separates three types of particles emitted byradioactive nuclei.

Radioactivity

He D P 22

42

AZ

AZ

Decay

Uses of Radioactivity

A smoke detector

Small amount of

radioactive material is

present

Ionizes the air between

the plates of a capacitor

Allows air to conduct

electricity

Presence of Smoke

Particles changes the

conductivity

e D P 011 A

ZAZ

Decay

Neutron “switches” into

a proton

Electron and

associated neutrino is

released

Other similar reactions

can occur

Positron emission

Electron capture

Positron capture

P P AZ

AZ

excited energystate

lower energystate

decay

Gamma knife

Use of Gamma Radiation

31.4.1. Which one of the following processes is considered radioactive decay?

a) a nucleus spontaneously emits a particle

b) a neutron collides with a uranium nucleus and breaks it into two pieces

c) a photon strikes a metal surface and causes an electron to be emitted

d) a proton and an alpha particle collide and form a new nucleus

e) single-celled organisms absorb nuclear particles

31.4.2. When bismuth undergoes alpha decay, what daughter nucleus is produced?

a) Bi

b) Tl

c) Au d) Au

e) Tl

Bi21183

20783

20781

20979

21179

20981

31.4.3. When francium undergoes alpha decay, what daughter nucleus is produced?

a) Rn

b) Ra

c) Po

d) At

e) At

Fr22387

22286

22388

22184

21985

22185

31.4.4. When osmium undergoes beta decay, what daughter nucleus is produced?

a) Ir

b) Ir

c) W

d) Re

e) Re

Os19176

19177

19077

18774

19175

18775

31.4.5. When krypton undergoes beta decay, what daughter nucleus is produced?

a) Rb

b) Br

c) Se

d) Sr

e) Rb

Kr8936

8837

8835

8534

8838

8937

31.4.6. By what method can a nucleus decay to a daughter nucleus with a larger atomic number?

a) There is no radioactivity process that will result in a daughter with a different atomic number than the parent.

b) There is no radioactivity process that will result in a daughter with a larger atomic number.

c) alpha decay

d) beta decay

e) gamma decay

31.4.7. Which one of the following occurs when Ra undergoes gamma decay?

a) The mass of the nucleus increases.

b) The mass of the nucleus decreases.

c) The atomic number increases.

d) The atomic number decreases.

e) The number of electrons decreases.

23688

Chapter 31:Nuclear Physics and Radioactivity

Section 5:The Neutrino

Fundamental Particles This will be discussed in greater detail in Ch 32 3 Types of Fundamental Particles

Bosons (Messenger Particles) Photon, W+, W-, Z, Gluons Gravitons (?)

Leptons electron, tau, muon, and corresponding

neutrinos Quarks

up, down, charm, strange, top, bottom All particles have corresponding antiparticles

For particles with no charge, the particles is its own antiparticle

During beta decay, energy is released. However, it is found that most beta particles do not have enough kinetic energy to account for all of the energy released.

The additional energy is carried away by a neutrino. The “flavor” is conserved as the neutrino is the anti-

electron neutrino

e e Pa Th 01

23491

23490

The Neutrino

Neutrino Facts Neutrinos have no electrical charge Have very little mass

Less than 0.0004% the mass of an electron! But due to their large numbers could be a

significant part of the mass of the universe. Do not interact easily with most forms of matter

More than 1 trillion pass through your body every second!

Very hard to detect Most pass through the entire earth without

reacting with anything! The average neutrino can penetrate more than

one light year of lead and still not react!

Chapter 31:Nuclear Physics and Radioactivity

Section 6:Radioactive Decay and Activity

The half-life of a radioactivedecay is the time in which ½of the radioactive nuclei disintegrate.

toeNN

2ln

21 T

Radioactive Decay

Example Half Lives

31.6.1. An isotope of cesium has a half-life of two years. If we had 100 grams of this isotope today, how much would we have left ten years from now?

a) about three grams

b) about six grams

c) about twelve grams

d) about twenty-five grams

e) about fifty grams

31.6.2. After 6400 years of undergoing alpha decay, a sample contains only 6.25% of the radium nuclei it initially had. What is the half-life of these radium nuclei?

a) 160 years

b) 6000 years

c) 3200 years

d) 800 years

e) 1600 years

31.6.3. In 1986, a nuclear accident occurred at Chernobyl in the former Soviet Union. During the accident, a radioactive isotope of iodine was released into the surrounding region that undergoes beta decay with a half-life of 8.040 days. How long did it take for the radioactivity from this iodine to be reduced to one percent of its initial value?

a) 64 days

b) 53 days

c) 48 days

d) 44 days

e) 32 days

31.6.4. What portion of a radioactive sample remains after two half-lives have passed?

a) None is left.

b) All remains.

c) one quarter

d) one half

e) three quarters

31.6.5. What portion of a radioactive sample remains after four half-lives have passed?

a) None is left.

b) 1/4

c) 1/8

d) 1/16

e) 1/32

31.6.6. After 6400 years of undergoing decay, a sample contains only 6.25% of the radium nuclei it initially had. What is the half-life of these radium nuclei?

a) 160 years

b) 6000 years

c) 3200 years

d) 800 years

e) 1600 years

Chapter 31:Nuclear Physics and Radioactivity

Section 7:Radioactive Dating

Using half lives

Conceptual Example 12 Dating a Bottle of Wine

A bottle of red wine is thought to have been sealed about 5 yearsago. The wine contains a number of different atoms, including carbon, oxygen, and hydrogen. The radioactive isotope of carbon is thefamiliar C-14 with ½ life 5730 yr. The radioactive isotope of oxygenis O-15 with a ½ life of 122.2 s. The radioactive isotope of hydrogenis called tritium and has a ½ life of 12.33 yr. The activity of eachof these isotopes is known at the time the bottle was sealed. However,only one of the isotopes is useful for determining the age of thewine. Which is it?

H-3 is useful as life of material is similar to ½ life

31.7.1. A centipede consumes a leaf at contains two 14C atoms and subsequently dies. How long will it take before these two atoms undergo beta decay?

a) 5730 years

b) 2865 years

c) 11 460 years

d) about one million years

e) It is not possible to predict exactly when these atoms will decay because of quantum uncertainties.

31.7.2. At an archeological dig, the remains of a saber-tooth tiger are found. In a carbon dating ( C has a half-life of 5730 years) test to determine the age of the cat, a scientist finds that the amount of

C is about 1/32 the amount of C in living animals. How long ago did this saber-tooth tiger die?

a) about 50 000 years ago

b) about 40 000 years ago

c) about 30 000 years ago

d) about 20 000 years ago

e) about 10 000 years ago

146

146

146

Chapter 31:Nuclear Physics and Radioactivity

Section 8:Radioactive Decay Series

Radioactive equation=Lays Chips Most of the time, many radioactive reactions occurs

in a long series. The sequential decay of one nucleus after another

is called a radioactive decay series

Example U-238 Decay

Chapter 31:Nuclear Physics and Radioactivity

Section 9:Radiation Detectors

A Geiger counter

Radiation Detectors

A scintillationcounter

Radiation Detectors