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Nuclear Physics and Radioactivity
At the beginning of the century (1900), not much was known about the atom. The
electron was discovered by J.J. Thomson in 1897. Thomson did not know much was
known about the electron and advanced the "plum pudding" model of the atom. The
number of electrons contained in an atom could not be determined. It wasn't until
Rutherford's famous experiment in 1911 that the atomic nucleus was described. Scientists
wondered if the nucleus had structure and if it did, what kind of structure did it have.
By the 1930's, our present nuclear model was developed. The nucleus is still not fully
understood today.
Structure and Properties of the Nucleus:
A nucleus can be considered to be made up of two types of particles--protons and
neutrons. These particles also have wave properties.
Proton The nucleus of the simplest atom, hydrogen. It has a positive charge of +q and a
mass of mp = 1.67 x 10-27 kg.
Neutron A particle found in the nucleus that is electrically neutral and that has a mass
almost identical to the proton. It was discovered in 1932 by James Chadwick. Thus, its
charge is q=0; its mass is mn = 1.6749 x 10-27 kg. Chadwick's discovery established that
the nucleus contained two types of particles -- protons and neutrons.
Nucleons The term that refers to the two constituent particles of a nucleus (protons and
neutrons).
Atomic Number The number of protons in a nucleus (designated by the letter Z).
Atomic Mass Number The total number of protons and neutrons (designated by the
letter A). The mass of a nucleus is very close to A times the mass of one nucleon.
Isotope Nuclei that contain the same number of protons but different numbers of
neutrons. Isotopes are generally described as "Carbon-12, Nitrogen-15, etc."
To denote a single nuclide, only A and Z are needed. Let X represent the symbol of the
element. Then the atom can be represented by AZX.
The total mass of a stable nucleus is always less than the sum of the masses of its
constituent particles. The nucleus is approximately spherical. The radius of the nucleus is
approximately r =(1.2 x 10-15 m)(A1/3)
Mass Defect The difference in the mass of a nucleus and the sum of the masses of its
constituent particles. For example, the mass of helium is measured to be 4.002602 u. The
total mass of its constituents (2 protons and 2 neutrons) is 4.032980 u. The mass defect of
helium is 0.030378 u.
Nuclear Binding Energy The amount of energy that must be put into a nucleus to break
it into its constituent particles. It is the energy equivalent of the mass defect found by
using E = mc2. For helium, the nuclear binding energy is equal to (0.030378 u)(931.5
MeV/u) = 28.30 MeV. If the mass of the nucleus was exactly equal to the sum of the
masses of its constituent particles, the nucleus would fall apart without any input of
energy. To be stable, the mass of the nucleus must be less than the mass of its constituent
particles, so that energy must by added to break it apart.
Unified atomic mass units (u) Used to denote nuclear masses. Carbon-12 is given the
exact value of mass of 12.000000 u. The mass of a proton is then 1.007276 u and a
neutron is 1.008665 u.
AP Free Response Questions Dealing with Mass Defect and Nuclear Binding
Energy:
1. Given a nuclear reaction and the masses of the reactants and products in u (atomic
mass units), you will be asked to calculate the mass defect and the energy
released.
2. Be able to convert nuclear binding energy for one reaction to energy in Joules.
Mass measured in electron volts Since mass and energy are related, 1 u = 1.6605 x 10-27
kg = 931.5 MeV.
We can also look at a nucleus in terms of the forces that hold it together. The electric
force described by Coulomb predicts that the nucleus should fly apart (since positive
charges repel other positive charges). Another short-range attractive force must be acting
within the nucleus. This force must be stronger than the electric force.
Strong Nuclear Force An attractive force that acts between all neucleons. Protons attract
each other via the strong nuclear force while they repel each other via the electric
(Coulombic) force. The strong nuclear force is the strongest force, but it only acts over
very short distances (less than 10-10 m). It is a short range force that is essentially zero
when nucleons are separated by more than 1015 m. If a nuclide contains too many or too
few neutrons relative to the number of protons, the binding of the nucleus is reduced and
it is unstable. Current thought is that the strong nuclear force is a "face" of the color force
between quarks.
 The color force is radically different than the electric force. As the distance between
quarks increases, the color force between them also increases. The color force predicts
that quarks cannot exist independently. In other words, it would take an infinite amount
of force to increase the distance between quarks to infinity. In the electric force, the force
decreases as the separation distance increases.
Stable nuclei tend to have equal numbers of protons and neutrons for nuclei with Z = to
about 30 or 40. If there are too many or too few neutrons relative to the number of
protons, the nuclei tends to be unstable. For nuclei with Z greater than 30 or 40, stable
nuclei have more neutrons than protons. There are no stable nuclei with Z greater than 83.
They are all radioactive. As Z increases, the electric repulsion increases. Nucleides with
large numbers of protons need more neutrons (which only exert the attractive strong
nucleur force) to overcome the electric repulsion between protons. For these very large
nuclei, no number of neutrons can overcome the electric repulsion between protons. All
elements with Z grater than 92 do not occur naturally.
Nuclear Reactions & Nuclear Decay
http://ithacasciencezone.com/chemzone/lessons/11nuclear/nuclear.htm
In 1896, Henri Becquerel discovered that a photographic plate was darkened in the
prescence of uranium. Marie and Pierre Curie isolated two radioactive substances,
polonium and radium. In 1899, Rutherford discovered that uranium compounds produced
three different kinds of radiation.
Types of particles involved in radioactive decay:
Radioactive Nuclei that decay, emitting radiation, are considered to be radioactive. In
other words, a nucleus that comes apart. A new element is produced through this decay.
Transmutation The changing of one element into another element via radioactive decay.
When unstable nuclei disintegrate, the must obey these laws of physics
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conservation of energy
conservation of electric charge
conservation of mass
Alpha Particle The particle emitted in alpha decay. It is essentially a helium nucleus. It
contains two protons and two neutrons. It has a charge of q=+2 and a mass of A=4.
When a nuclei decays by emitting an alpha particle, the number of protons is reduced by
two and its mass is reduced by four. Alpha particles are emitted by very large nuclei
where the strong nuclear force is insufficient to hold the nuclei together. It is abbreviated
 or
.
Beta Particle The particle emitted in beta decay. Beta particles are (negative) electrons
emitted by the nucleus. It is not an orbital electron, but one created in the nucleus by the
decay of a neutron into a proton and an electron. It has a charge of q=-1 and essentially
no mass. Beta particles are emitted by nuclei that have too many neutrons relative to the
number of protons. It is abbreviated  or
.
Weak Nuclear Force Involved in the production of a beta particle in the nucleus.
There are four fundamental forces in nature
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electromagnetic force
gravitational force
strong nuclear force
weak nuclear force
During beta decay, energy is released. It was experimentally found that not all the energy
could be accounted for. The kinetic energy of the electrons produced in beta decay were
measured and a range of KE values found. Careful measurements showed that energy,
linear momentum, and angular momentum did not seem to be conserved. In 1930, Pauli
proposed the presence of the neutrino that was "carrying off" the energy, momentum, and
angular momentum. It was discovered in 1956. The neutrino has zero charge, and zero
rest mass (though it is hypothesized that it could have a very small rest mass).
Gamma Radiation Radiation emitted in gamma decay. Gamma radiation is composed of
high-energy photons. It is emitted by excited state nuclei. Gamma radiation has no charge
and no mass. It is abbreviated by .
Positron A positive electron produced in the nucleus by the decay of a proton into a
positron and a neutron. It has a charge of q=+1 and essentially no mass. They are emitted
by nuclei that have too few neutrons relative to their number of protons. It is abbreviated
by  or
.
Proton The nucleus of a hydrogen atom. The symbol is p or
.
Neutron The symbol is n or
.
In AP, you are responsible for knowing common names for the three isotopes of
hydrogen. A proton (H-1) has no neutrons and one proton. A dueteron (H-2) has one
neutron and one proton. Sometimes this is referred to as deuterium. Tritium (H-3) has
two neutrons and one proton.
In all radioactive decay, the classical conservation laws hold. Energy, linear momentum,
angular momentum, and electric charge are conserved. Also, the baryon numbers and
lepton numbers are conserved. When balancing a nuclear reaction, mass and charge are
conserved.
Rate of Decay:
Decay Constant,  A constant of proportionality.
Half-life (T1/2) The time it takes for half the original amount of the substance (No) to
decay.
Mass-energy equivalence One of the most profound results of Einstein's Theory of
Relativity was the fact that mass could be converted into energy and vice versa. The
equation is well-known, or E = mc2
Once, an atom was thought to be the smallest particle into which matter could be divided.
Then, Rutherford found that an atom was composed of protons and neutrons. The
electron was discovered. Now, physicists believe that particles out of which matter is
composed can be grouped into two families, quarks and leptons.
Quark Protons and neutrons are composed of quarks. A combination of three quarks
compose a proton. A different combination of three quarks compose a neutron. Particles
that are composed of three quarks are called baryons.
Lepton Examples of leptons are electrons and neutrinos.
There are also particles that "carry" or transmit forces. The electromagnetic force is
carried by photons. The gravitational force is carried by gravitons (not yet detected). The
strong nuclear force binds quarks into protons and neutrons and is carried by gluons. The
weak nuclear force is carried by three particles called bosons.
Each particle has an associated antiparticle. The positron is the electron's antiparticle. For
every quark, there is an antiquark. Particles composed of quark, antiquark pairs are called
mesons.
Physicists are currently trying to create a Grand Unified Theory. In this theory, the four
fundamental forces, gravitational, strong nuclear, weak nuclear, and electromagnetic,
were originally one force at the universe's beginning. The electromagnetic and the weak
nuclear forces were unified into the electroweak force in the 1970's.
Nuclear Energy
In 1934, Enrico Fermi and Emilio Segré bombarded uranium with neutrons, producing
new radioactive isotopes. In 1939, German scientists Otto Hahn and Fritz Strassmann
found that barium was produced by bombarding uranium with neutrons. Lisa Meitner and
Otto Frisch proposed that the neutrons caused the uranium to divide into two smaller
nuclei, accompanied by a tremendous release of energy.
Fission A division of a nucleus into two or more smaller daughter nuclei. For U-235, the
products of the fission reaction are Ba-141, Kr-92, three neutrons, and a tremendous
release of energy.
Chain Reaction Neutrons produced by the fission of one nucleus induce the fission of
other nuclei.
Cricical mass The minimum mass of uranium needed to produce a self-sustaining chain
reaction.
Fusion Two or more nuclei combine to form a larger nucleus. The sun produces its
energy by nuclear fusion. In our sun, the net effect is results in four H-1 decaying to form
a helium neucleus, 2 positrons, 2 neutrinos, two gamma rays, and energy.
AP Free Response Questions: Since the percentage on nuclear physics decreased to 3%
in 2002, I do not anticipate much emphasis on nuclear physics in free response questions
in the future.
1. In the past, a radioactive decay was described with the amount of emitted energy
quoted. From this information, determine the atomic number of one of the
particles and the velocity of emitted particle. Be able to calculate the de Broglie
wavelength of the emitted particle.
2. Describe where the energy of an emitted particle comes from.
3. Describe how a quoted reaction would be affected if a different type of particle
was emitted.
4. Half life is no longer asked on the AP exam.
AP Multiple Choice Questions: Since the percentage on nuclear physics decreased to
3% in 2002, I predict that the only emphasis on nuclear physics in the future will most
likely be in multiple choice questions.
1. Be able to complete nuclear reactions, predicting the atomic mass and number of
the product or reactant.
2. Know how the mass and the energy of products and reactants relate.
3. Be able to identify fission &/or fusion reactions.
4. Know the characteristics of the common naturally occuring radioactive particles.
Artificial transmutation is using nuclear reactions to change the atomic number of the
nucleus by changing one element into another. This process has produced many new
elements beyond the naturally occurring ones in the periodic table.
Nuclear Reactors
Nuclear fission power plant
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Nuclear Power Plant simulation -- prevent a disaster!
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Nuclear Power plant Virtual tour
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Moderator slows down neutrons produced in chain reactions so they can be
more easily absorbed by other nuclie so fission continues.
Control rods absorb neutrons, controlling the rate of reaction.
Breeder reactors are ones in which some of the neutrons produced in the fission
of U-235 produce plutonium. This plutonium can be used in an atomic bomb.
What is the universe made of? How did the universe come to be the way that it is?
New particles began to be discovered; this discovery continues today. Today, there are
several hundred known particles.
These particles can be categorized in terms of:
1. Spin (the spin quantum number)
o Fermions have half-integer values (electrons, protons, neutrons, etc)
o Bosons have integer spin values (photon)
2. Forces
o Hadrons are particles upon which the strong force acts (protons, neutrons,
pions, etc.)
o Leptons are particles on which the strong force does not act (electrons,
neutrinos)
There are three generations of leptons: electron and electron
neutrino, muon and muon neutrino, and tauon and tauon neutrino.
The leptons are considered to be true elementary particles since
they do not break down into smaller entities.
3. Particles and antiparticles
o Every particle has a corresponding antiparticle with the same mass and
spin but opposite charge
o When a particle encounters its antiparticle, they annihilate each other.
o There are three elementary particles which compose all matter: quarks,
electrons, and gauge bosons. There are three observed particles: hadrons,
electrons, and gauge bosons.
Quark model Hadrons are composed of elementary particles called quarks. There are
three flavors of quarks.(Remember, each particle also has an antiparticle). As yet, an
individual quark has not been seen.
Particle Symbol Charge
up
u
+ 2/3
down
d
- 1/3
strange s
- 1/3
charm
c
+ 2/3
bottom b
- 1/3
top
+ 2/3
t
Baryons are combinations of three quarks. Mesons are a quark and antiquark pair. For
example, a proton (with charge of +1) is up,up,down and a neutron (with charge of 0) is
up, down, down. If you look at beta decay in terms of the quark model, a neutron (udd) is
converted into a proton (uud), or a down quark is changed into an up quark.
The four fundamental forces have force messanger particles.
1. Electromagnetic force - two electrons exert Coulombic forces on each other. Each
electron learns of the other's presence by exchanging photons. The photon is the
messenger particle of the EM force.
2. Weak nuclear force. The messenger particles are the W and Z bosons. According
to the electroweak theory, the electromagnetic and weak forces are different
"faces" of the same force, called the electroweak force.
3. Gravitational force. The messenger particle is the graviton.
4. Strong nuclear force. The messanger particle is called the gluon. Each flavor of
quark comes in three varieties, called colors (red, yellow, blue and their
anticolors). Quarks interact via the color force. For example, in baryons, three
varieties must combine to produce white (red, yellow, and blue). In mesons,
quarks only combine in neutral colors (ex. red and antired).
Why are a few particles dominant in our universe? Why do we live in a universe of
particles, not antiparticles? We live in a universe with a low temperature. The most
distant object that we see is a quasar, 13 x 109 years away.
The Big Bang occurred everywhere at the same time in our universe. Here is a theory
describing the early moments of our universe.
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time=0 to 10-43 seconds
o Space and time are disconnected and the laws of physics as we know them
do not hold
o At time= 10-43 seconds, Temp=1023 K
time= 10-43 seconds to 10-36 seconds
o Strong, weak, and electromagnetic force act as a single force; gravity acts
seperately
time= 10-36 seconds to 10-10 seconds
o Strong nuclear force "freezes out."
time= 10-10 seconds to 10-5 seconds
o All four forces act seperately.
o The universe is a soup of quarks, leptons, and photons.
time= 10-10 seconds to three minutes
o Quarks combine to form mesons and baryons
o Matter and antimatter annihilate each other, wiping out antimatter, and
leaving a slight excess of matter
time= 3 min to 105 years
o Protons and neutrons form He-4, He-3, H-2, and Li-7.
o Universe is a plasma of nuclei and electrons
time= 105 years to the present
o Atoms form
o Universe becomes transparent to photons
Nuclear Physics Sample Problems
Nuclear Reactions and Half Life Sample Problems
1. N-13 has a half life of ten minutes. If you start with 2 grams, how much remains
after 40 minutes?
2. After 10.4 hours, you have 0.625 mg remaining of an original 10 mg sample of
Mn-56. What is its half-life?
3. The half-life of Ge-68 is 9 months. How much remains of an original sample size
of 35 g after 3.0 years?
4. The half-life of a radioactive substance is 4.5 days. 3 g remains after 2 days of
decay. What was the original sample size?
5. The decay constant of a given nucleus is 5.4 x 10-3/sec. What is its half-life? How
much remains of an initial 100 g sample after 6 h?
6. 45 g of an original 1 kg sample of a radioactive material remains after 2.2 h. What
is the decay constant of the radioactive material?
7. 0.30 g remains of an original 1 g sample of a radioactive substance after 45 h.
What is the half-life?
8. You have 2 g of an original 40 g sample after 50 min. What is the half-life?
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Nuclear Physics Homework
Nuclear Physics Homework
1. 250 g of I-131 emits beta particles in its radioactive decay. Its half life is 8 days.
How much remains after 16 days? Write the decay equation. Ans: 62.5 g
2. The half life of Sr-90 is 28 years. If 60 g of Sr-90 is found in a soil sample,
estimate the amount in the sample after 84 years. Write is decay equation (it emits
a beta particle). Ans: 7.5 g
3. Sr-82 has a half life of 25 days. If you begin with a 140 g sample, how many days
later will you only have 17.5 g? Ans: 75 d
4. The half life of a certain isotope is 20 h. How much of an original sample of 320 g
remains after 80 h? After 5 d? Ans: 20 g; 5 g
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