Chapter 29

Nuclear Physics

Properties of Nuclei• All nuclei are composed of protons and neutrons

(exception: ordinary hydrogen)

• Nucleon is a generic term used to refer to either a proton or a neutron

• The atomic number, Z, equals the number of protons in the nucleus

• The neutron number, N, is the number of neutrons in the nucleus

• The mass number (not the same as the mass), A, is the number of nucleons in the nucleus: A = Z + N

Properties of Nuclei• Symbol:

• X is the chemical symbol of the element

• Example:

• Mass number is 27; atomic number is 13; contains 13 protons and 14 = 27 – 13 neutrons

• The Z may be omitted since the element can be used to determine Z

• The nuclei of all atoms of a particular element must contain the same number of protons

XAZ

Al2713

Properties of Nuclei• The nuclei may contain varying numbers of neutrons

• Isotopes of an element have the same Z but differing N and A values. For example:

• The proton has a single positive charge, +e (e = 1.602 177 33 x 10-19 C)

• The electron has a single negative charge, -e

• The neutron has no charge, which makes it difficult to detect

C116 C126 C136 C146

Mass• It is convenient to express masses using unified mass

units, u, based on definition that the mass of one atom of C-12 is exactly 12 u:

1 u = 1.660 559 x 10-27 kg

Masses

Particle kg u

Proton 1.6726 x 10-27 1.007276

Neutron 1.6750 x 10-27 1.008665

Electron 9.109 x 10-31 5.486x10-4

The Size of the Nucleus• From scattering experiments, Rutherford found an

expression for how close an alpha particle moving toward the nucleus can come before being turned around by the Coulomb force

• The KE of the particle must be completely converted to PE

• d gives an upper limit for the sizeof the nucleus (e.g., for gold, d = 3.2 x 10-14 m and for silver,d = 2 x 10-14 m)

r

qqk

mve

212

2

d

Zeeke

))(2( 2

24

mv

Zekd e

The Size of the Nucleus• Such small lengths are often expressed in femtometers

where 1 fm = 10-15 m Also called a fermi

• Since the time of Rutherford, many other experiments have concluded that most nuclei are approximately spherical with the average radius of

• ro = 1.2 x 10-15 m

13

or r A

Enrico Fermi1901 – 1954

Chapter 29Problem 7

(a) Find the speed an alpha particle requires to come within 3.2 × 10−14 m of a gold nucleus. (b) Find the energy of the alpha particle in MeV.

Nuclear Stability

• There are very large repulsive electrostatic forces between protons

• These forces should cause the nucleus to fly apart

• The nuclei are stable because of the presence of another, short-range force, called the nuclear force

• This is an attractive force that acts between all nuclear particles

• The nuclear attractive force is stronger than the Coulomb repulsive force at the short ranges within the nucleus

Nuclear Stability• Light nuclei are most stable if

N = Z

• Heavy nuclei are most stable when N > Z

• As the number of protons increase, the Coulomb force increases and so more nucleons are needed to keep the nucleus stable

• No nuclei are stable when Z > 83

Radioactivity• Radioactivity is the spontaneous emission of radiation

• Radioactivity is the result of the decay (disintegration) of unstable nuclei

• Three types of radiation can be emitted

• 1) Alpha particles: 4He nuclei)

• 2) Beta particles: either electrons or positrons (a positron is the antiparticle of the electron, similar to the electron except its charge is +e)

• 3) Gamma rays: high energy photons

Penetrating Ability of Particles

• Alpha particles: barely penetrate a piece of paper

• Beta particles: can penetrate a few mm of aluminum

• Gamma rays: can penetrate several cm of lead

The Decay Constant• The number of particles that decay in a given time is

proportional to the total number of particles in a radioactive sample

ΔN = - λ N Δt

• λ: the decay constant; determines the rate at which the material will decay

• The decay rate or activity, R, of a sample is defined as the number of decays per second

NR N

t

Decay Curve

• The decay curve follows the equation

N = No e- λt

• Another useful parameter is the half-life defined as the time it takes for half of any given number of radioactive nuclei to decay

1 2

ln 2 0.693T

Decay Curve

1 2

ln 2 0.693T

teNN 02/1

00

2TeN

N

2/1

2

1 Te 22/1 Te

2ln2/1 T

Units• The unit of activity, R, is the Curie, Ci: 1 Ci = 3.7 x 1010

decays/second

• The most commonly used units of activity are the mCi and the µCi

• The SI unit of activity is the Becquerel, Bq: 1 Bq = 1 decay/second (therefore, 1 Ci = 3.7 x 1010 Bq)

Maria Skłodowska-Curie1867 – 1934

Antoine Henri Becquerel1852 – 1908

Chapter 29Problem 24

A building has become accidentally contaminated with radioactivity. The longest-lived material in the building is strontium-90. (The atomic mass of is 89.907 7.) If the building initially contained 5.0 kg of this substance, and the safe level is less than 10.0 counts/min, how long will the building be unsafe?

Decay – General Rules

• When one element changes into another element, the process is called spontaneous decay or transmutation

• The sum of the mass numbers, A, must be the same on both sides of the equation

• The sum of the atomic numbers, Z, must be the same on both sides of the equation

• Conservation of mass-energy and conservation of momentum must hold

Alpha Decay• When a nucleus emits an alpha particle it loses two

protons and two neutrons (N decreases by 2; Z decreases by 2; A decreases by 4)

• Symbolically

• X: parent nucleus; Y: daughter nucleus

• Example: decay of 226 Ra (half life is1600 years)

• Excess mass is converted intokinetic energy

• Momentum of the two particles is equal and opposite

HeYX AZ

AZ

42

42

HeRnRa 42

22286

22688

Beta Decay• During beta decay, the daughter nucleus has the same

number of nucleons as the parent, but the atomic number is changed by one

• Symbolically:

• The emission of the electron is from the nucleus, which contains protons and neutrons

• The process occurs when a neutron is transformed into a proton and an electron

• The energy must be conserved: the energy released in the decay process should almost all go to kinetic energy of the electron (KEmax)

eYX

eYXA

ZAZ

AZ

AZ

1

1

Beta Decay• Experiments showed that few electrons had this

amount of kinetic energy

• To account for this “missing” energy, Pauli proposed the existence of another particle, which Fermi later named the neutrino

• Properties of the neutrino:

• Zero electrical charge• Mass much smaller than the

electron, probably not zero• Spin of ½• Very weak interaction with

matter

Beta Decay• Symbolically

is the symbol for the neutrino; is the symbol for the antineutrino

• Therefore, in beta decay, the following pairs of particles are emitted: either an electron and an antineutrino or a positron and a neutrino

eYX

eYXA

ZAZ

AZ

AZ

1

1

Gamma Decay• Gamma rays are given off when an excited nucleus

“falls” to a lower energy state (similar to the process of electron “jumps” to lower energy states and giving off photons)

• The gamma ray photons are very high in energy relative to light

• The excited nuclear states result from “jumps” made by a proton or neutron

• The excited nuclear states may be the result of violent collision or more likely of an alpha or beta emission

Gamma Decay• Example of a decay sequence

• The first decay is a beta emission

• The second step is a gamma emission

• The C* indicates the Carbon nucleus is in an excited state

• Gamma emission doesn’t change either A or Z

CC

eCB126

126

126

125

*

*

Natural Radioactivity• There are unstable nuclei found in nature, which give

rise to natural radioactivity

• Nuclei produced in the laboratory through nuclear reactions exhibit artificial radioactivity

• Three series of natural radioactivityexist (see table 29.2):1) Uranium2) Actinium3) Thorium (processes through aseries of alpha and beta decays andends with a stable isotope oflead, 208Pb)

• Structure of nuclei can be changed by bombarding them with energetic particles

• These changes are called nuclear reactions

• As with nuclear decays, the atomic numbers and mass numbers must balance on both sides of the equation

• E.g., alpha particle colliding with nitrogen:

• Balancing the equation allows for the identification of X, so the reaction is

Nuclear Reactions

4 14 12 7 1He N X H 17 17

8 8X X O

4 14 17 12 7 8 1He N O H

Chapter 29Problem 39

Identify the unknown particles X and X’ in the following nuclear reactions: X + He4

2 → Mg2412 + n1

0

U23592 + n1

0 → Sr9038 + X + 2 n1

0

2 H11 → H2

1 + X + X’

Answers to Even Numbered Problems

Chapter 28:

Problem 4

ρn/ρa = 8.6 × 1013

Answers to Even Numbered Problems

Chapter 28:

Problem 8

a) 1.9 × 10-15 mb) 7.4 × 10-15 m

Answers to Even Numbered Problems

Chapter 28:

Problem 10

(a) 1.11 MeV/nucleon (b) 7.07 MeV/nucleon (c) 8.79 MeV/nucleon (d) 7.57 MeV/nucleon

Answers to Even Numbered Problems

Chapter 28:

Problem 18

(a)8.06 d(b) It is probably 131

53I

Answers to Even Numbered Problems

Chapter 28:

Problem 20

2.29 g

Answers to Even Numbered Problems

Chapter 28:

Problem 38

42He, 4

2He

Answers to Even Numbered Problems

Chapter 28:

Problem 42

a) 105B

b) –2.79 MeV