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Chapter 11
Nuclear Physics
The nucleus
 The nucleus occupies the very center of the
atom.
 It is tiny yet incredibly dense:

More than 99.9% of the atom’s mass is
compressed into roughly one-trillionth of its
total volume.
 The nucleus is impervious to the chemical
and thermal processes that affect its
electrons.
2
The nucleus, cont’d
 The nucleus contains two type of particles.

The proton and neutron.
 These particles have a mass about 1,840
times the
electron mass.
3
The nucleus, cont’d
 It is convenient to introduce an appropriate
unit of mass, called the atomic mass unit, u:
1 u  1.66 10
27
kg
4
The nucleus, cont’d
 Recall that the number of protons in the
nucleus is given by the atomic number, Z.

This number identifies the type of atom.
 The neutrons play a smaller role in
determining the properties of the atom.

Their effect is mainly on the atom’s mass.
 The neutron number, N, is the number of
neutrons contained in a nucleus.
5
The nucleus, cont’d
 The mass number, A, is the total number of
protons and neutrons in a nucleus.
AZ N

We omit the electron’s mass because it so small
compared to the proton’s and neutron’s.
 Protons and neutrons are collectively referred
to as nucleons.
6
The nucleus, cont’d
 Each element has a given number of protons
but can have different numbers of neutrons.
 Each different possible “type” of atom is
called an isotope.

Isotopes of a given element have the same
number of protons in the nucleus but a
different number of neutrons.
 Different isotopes have essentially the same
atomic properties but different nuclear
properties.
7
The nucleus, cont’d
 Most of the 114 different elements have
several isotopes.


Some have only a few: hydrogen has 3.
Others have many: iodine, mercury and silver
have more than 20.
 More than 2,500 different isotopes have been
identified and studied.

Only about 300 of these occur naturally.
8
The nucleus, cont’d
 The different isotopes of carbon are
carbon-12, carbon-13, and carbon-14.
 The different isotopes of hydrogen have
special names:


hydrogen-2 is called deuterium.
hydrogen-3 is called tritium.
 Isotopes play no role in chemical reactions.
 They are pivotal for understanding nuclear
reactions.
9
The nucleus, cont’d
 We use a special notation to represent each
isotope.



The element’s chemical symbol is used.
A subscript to the left of the chemical symbol
represents the atom’s atomic number Z.
A superscript to the left of the chemical symbol
represents the atom’s atomic mass A.
Helium-4
Carbon-12
4
2
12
6
He
C
Carbon-14
Uranium-235
14
6
235
92
C
U
10
The nucleus, cont’d
 Notice that the subscript, the atomic number,
must always agree with the chemical symbol.

If the subscript is 6, the symbol must be for
carbon, C.
 The number of neutrons can be found by
subtracting the atomic number from the
atomic mass:
235
92
U  N  235  92  143
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The nucleus, cont’d
 We use a similar notation for atomic particles.

Proton
1
1
Electron
0
-1
n
p
e
The superscript is the mass in atomic units.


Neutron
1
0
Zero for the electron since it is so small.
The subscript is the electric charge.
12
The nucleus, cont’d
 The nuclear strong force is responsible for
binding protons in the nucleus against the
electromagnetic force.



Since protons are positively charged, they
repel each other.
At such short range, the electric force is
tremendous.
The nuclear force that “overpowers” the
electric force was therefore given the name
the strong force.
13
Radioactivity
 Radioactivity, also called radioactive decay,
occurs when an unstable nucleus emits
radiation.
 Isotopes with unstable nuclei are called
radioisotopes.

The majority of all isotopes are radioactive.
14
Radioactivity, cont’d
 This diagram shows
the number of
neutrons versus the
number of protons
in the isotopes.

Stable isotopes are
indicated by a small
square.
15
Radioactivity, cont’d
 There are three types of nuclear radiation:

alpha radiation (a) are made of helium nuclei.



beta radiation (b) are made of high energy
electrons.


Two protons and two neutrons.
Has a positive electric charge.
Has a negative electric charge.
gamma radiation (g) is EM radiation.

Has no electric charge.
16
Radioactivity, cont’d
 The type of radiation can be determined by
passing it through a magnetic field.
 Since each type
has a different
electric charge,
they are deflected
differently by the
magnet.
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Radioactivity, cont’d
 The most common type of radiation detector
is the Geiger counter.



The radiation ionizes the gas in a cylinder.
The freed electrons are acceleration to the red
wire and
produce a
current pulse.
That pulse is
counted.
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Alpha decay
 Alpha decay occurs when an unstable
nucleus ejects an alpha particle.

Recall that an alpha particle is just a helium
nucleus.

two protons and two neutrons.
alpha particle : a or
4
2
He
 The nucleus did not contain an alpha particle.

This is just a stable collection of particles that
can be ejected.
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Alpha decay, cont’d
 The emission of an alpha particle:

Reduces the number of particles by 4.

The nuclear mass is reduced by 4 u.

It reduces the number of protons by two, and

It reduces the number of neutrons by two.
A  A 4
Z Z 2
N  N 2
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Alpha decay, cont’d
 Here is a diagram illustrating alpha decay.


We start with an unstable plutonium nucleus.
We obtain:


a uranium nucleus, and
an alpha particle.
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Alpha decay, cont’d
 Alpha decay results in a drastic change in the
mass of the nucleus.

It typically occurs in radioisotopes with high
atomic numbers.
 The ejected alpha particle is quickly absorbed
by matter.

A sheet of paper can stop it.
22
Example
Example 11.1
The isotope radium-226 undergoes alpha
decay. Write the reaction equations, and
determine the identity of the daughter
nucleus.
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Example
Example 11.1
ANSWER:
The reaction is:
226
88
Ra  He 
4
2
226  4
88 2
?
 He 
222
86
?
 He 
222
86
Rn
4
2
4
2
24
Beta decay
 Beta decay occurs when an unstable nucleus
ejects a beta particle.

Recall that an beta particle is just an electron
beta particle : b or
0
1
e
 The nucleus does not contain any electrons.

A neutron is spontaneously converted into an
electron and a proton.

The electron is ejected at high speed while the
proton remains in the nucleus.
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Beta decay, cont’d
 The emission of an beta particle:

Keeps the atomic mass the same but changes
the type of nucleons.

The nuclear mass is not changes.

It increases the number of protons by one, and

It reduces the number of neutrons by one.
A A
Z  Z 1
N  N 1
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Beta decay, cont’d
 Here is a diagram illustrating beta decay.


We start with a carbon-14 nucleus
We obtain:


a nitrogen-14 nucleus, and
an beta particle (electron).
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Beta decay, cont’d
 Beta decay results in (essentially) no change
of the nuclear mass

It is typically a rearranging of the type of
nucleons toward a more stable configuration.
 The ejected beta particle passes easily
through most matter.

A sheet of lead provides a good shield against
beta particles.
28
Example
Example 11.2
The isotope iodine-131 undergoes beta decay.
Write the reaction equations, and determine
the identity of the daughter nucleus.
29
Example
Example 11.2
ANSWER:
The reaction is:
131
53
0
1
I  e
131
54
?
 e
131
54
Xe
0
1
30
Gamma decay
 Gamma decay occurs when an excited
nucleus ejects a gamma particle.

Recall that an gamma particle is just a photon
in the gamma ray part of the EM spectrum.
gamma particle : g
 The nucleus does not contain any photons.

This decay is similar to an excited atom
emitting a photon.
31
Gamma decay, cont’d
 The emission of an gamma particle:

Keeps the atomic mass and atomic numbers
the same.

The nuclear mass is not changes.

The number of protons remains the same.

The number of neutrons remains the same.
A A
Z Z
N N
32
Gamma decay, cont’d
 Here is a diagram illustrating gamma decay.


We start with an excited strontium nucleus.
We obtain:


a strontium nucleus in a lower energy level, and
an gamma particle.
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Gamma decay, cont’d
 Gamma decay results in no change of the
nuclear mass

It is simple the emission of a photon due to the
nucleus being in an excited state.
 The ejected gamma particle passes easily
through almost all matter.

A brick of lead provides a reasonably good
shield against gamma particles.
34
Applications
 Nuclear medicine makes use of radioisotopes
for diagnosis and treatment.


Introducing a radioactive element into the
blood stream allows the blood flow to be
followed.
Irradiating a tumor kills the tumor cells.
 Gamma radiation is very effective for
sterilization.

It kills virtually any organism it strikes.
35
Applications, cont’d
 Some smoke detectors use radioactive
samples to monitor air particles.



The sample ionizes the air which establishes a
current.
The ions attach to smoke particles and
effectively
reduce the
current.
The alarm
then triggers.
36
Half-life
 Radioactive decay is a random process.

An unstable isotope will decay but the exact
amount of time until it decays is unknown.
 To overcome this, we talk about how much of
a radioactive sample decays in a certain
amount of time.
 Half-life is the time it takes for half the nuclei
in a sample of a radioisotope to decay.

The time interval during which each
nucleus has a 50% probability of decaying.
37
Half-life, cont’d
 This table shows the
half-life for several
isotopes.

Notice that the halflives range from
extraordinarily short
(2×10-21 s) to
extremely long
(4.5×109 yr).
38
Half-life, cont’d
 It is infeasible to count how many nuclei are
left after a given time interval.
 But a Geiger counter can indicate how quickly
radioisotopes are decaying.
39
Half-life, cont’d
 Knowing the half-life is very useful.

Smoke detectors routinely use americium-241
since it has a half-life of 432 yrs.


Enough time to allow for proper operation for the
devices lifetime.
Nuclear medicine uses technetium-99 since it
emits gamma rays with a half-life of 6 hours.

More than enough time to track its passage
through the body.
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Carbon dating
 The regular rate of decay of a radioisotope
can be used to measure time.
 Carbon-14 dating uses the decay-rate of
carbon-14 to determine how long ago an
organism died.
 Carbon-14 is naturally created from nitrogen
in the upper atmosphere.
41
Carbon dating, cont’d
 While a plant is alive, it absorbs carbon
dioxide from the air.

CO2 could be made from C-12, C-13 or C-14.
 Some animals eat the plant, while other
animals eat the plant-eater.
 So each organism is continuously
replenishing the amount of C-14 in its body.
 Once the organism dies, no more C-14 is
consumed so the level of C-14 begins to
decrease.
42
Carbon dating, cont’d
 This process can be used to determine how
long ago an organism died.



We know the average amount of C-14 in a
living organism.
We can measure the C-14 in a specimen.
Comparing the values and knowing the halflife, gives information on how long ago it died.
43
Nuclear binding energy
 Imagine dismantling a nucleus by removing
each proton and neutron, one at a time.
 Measure the amount of work required to
remove each nucleon.
 The amount of energy required to assemble
the nucleus equals the work required to
disassemble it.
 This amount of energy is called the binding
energy.
44
Nuclear binding energy, cont’d
 A convenient amount of energy is the amount
of binding energy per nucleon.
45
Nuclear binding energy, cont’d
 Nuclei with mass numbers around 50 have
the highest binding energy per nucleon.
 This means the protons and neutrons are
more tightly bound to the nucleus.

The nucleus is very stable.
 The idea of a nucleon being bound to the
nucleus is similar to a ball resting in a hole.

You have to do work on the ball to get it out of
the hole.
46
Nuclear binding energy, cont’d
 If the nucleons are not tightly bound to the
nucleus, a collision with another particle could
split the nucleus.

A neutron might impact uranium-235 to create
barium-141 and krypton-92 (and three extra
neutrons).
 Such a process is called nuclear fission.
 Energy is released during this process.
47
Nuclear binding energy, cont’d
 If two smaller nuclei collide, they might be
able to increase their binding energy if they
“stick” together.

Hydrogen-1 and hydrogen-2 might combine to
form helium-3.
 Such a process is called nuclear fusion.
 Energy is also released in this process.
48
Nuclear binding energy, cont’d
 Imagine combining a proton and a neutron.


proton has 1.00785 u.
neutron has 1.00869 u.
 After bonding,
the combination
has less mass
than the two
individual
nucleons.

2.01410 u rather
than 2.01654 u.
49
Nuclear binding energy, cont’d
 Einstein provided the reason for this:
E  mc
2
 This formula means that energy and mass
are different forms of the same quantity.


Energy can be converted into mass.
Mass can be converted into energy.
 This means that a hotter object (more energy)
has more mass than the same object at a
cooler temperature (less energy).
50
Nuclear binding energy, cont’d
 This difference in mass between individual
nucleons and their combination, means we
can liberate enormous amounts of energy.
E  mc
2

  0.00244 u  3 10 m/s

 4.0504 10
 3.65 10
13
30
J.
8


2
kg 9 10 m /s
16
2
2

51
Nuclear fission
 Nuclear fission is the process by which
nuclei split apart by absorbing a neutron.


Fission is commonly accomplished by
bombarding the radioisotope with neutrons.
But alpha particles, gamma rays and protons
have also proved successful.
 The resulting fragments are called fission
fragments.
52
Nuclear fission, cont’d
 Two possible fission reactions of uranium-235
are:
1
0
n
235
92
U
236
92

141
56
1
0
n
235
92
U
236
92

140
54
U

Ba  Kr  3 n
92
36
U
1
0

Xe  Sr  2 n
94
38
1
0
53
Nuclear fission, cont’d
 The amount of energy released during the
fission of one U-235 nucleus is 215 million
electron-Volts (about 3.4×10-11 joules).
 By comparison, the average energy involved
in chemical process, e.g., metabolism in your
body, is about 10 electron-Volts fro each
molecule involved.
54
Nuclear fission, cont’d
 Two other important aspects of fission:

The possible fission fragments are typically
radioactive.



The ratio of neutron to protons is too high for
stability.
These fragments are responsible for the
radioactive fallout from nuclear explosions.
The neutrons released by this process can
cause fission in other nuclei.

This process is called a chain reaction.
55
Nuclear fission, cont’d
 An atomic bomb can be created by increasing
the density of radioisotopes so that a chain
reaction begins.
 One way to accomplish this is to force
together two pieces of uranium by an
conventional
explosive.

You have a
critical mass
or U-235.
56
Nuclear fission, cont’d
 Another approach is to
cause a single piece of
radioactive sample to
reach critical mass by
compressing it.

This type of bomb
was dropped on
Nagasaki.

The other was
dropped on Hiroshima.
57
Nuclear fission, cont’d
 Nuclear power plants need to be able to
control the reaction rate so a chain reaction
does not occur.
 First, a less-enriched sample of uranium is
used.
58
Nuclear fission, cont’d
 Second, control rods are used to limit the
number of neutrons that can participate in the
fission process.
59
Nuclear fusion
 Nuclear fusion is the process of combining
two nuclei to form a larger nucleus.
 Some common reactions are:
H  H  H  n  3.3 MeV
1
H  H  He  0 n  17.6 MeV
2
3
1
1 H  2 He  He  1 p  18.3 MeV
2
1
2
1
2
1
3
1
3
2
4
2
4
2
1
0
60
Nuclear fusion, cont’d
 Energy is released in each case because the
total mass of the nucleons after the fusion is
less that the total mass before.
61
Nuclear fusion, cont’d
 Stars obtain most of their energy from a
natural fusion reaction in the star’s interior.
 At the Sun’s core:


the temperature is around 15 million degrees
Celsius, and
the pressure is over one billion atmospheres.
 These conditions force the hydrogen to fuse
into helium.

Each second, more than 4 million tons of
matter are converted into energy.
62
Nuclear fusion, cont’d
 Thermonuclear weapons fuse hydrogen to
generate their energy.
 To obtain the proper conditions for fusion,
they use a nuclear fission explosion to trigger
the fusion.

A hydrogen bomb is to an atomic bomb what a
stick of dynamite is to a firecracker.
63
Nuclear fusion, cont’d
 Controlled fusion is a technically challenging
problem.
 The conditions which must be met are:

The nuclei must be raised to extremely high
temperature.


The challenge here is to prevent such a hot
material from contacting the confinement vessel.
The must be sufficient density to maintain the
fusion process.

The plasma must be kept sufficiently dense so
there are sufficient number of fusions.
64
Nuclear fusion, cont’d
 A current approach to accomplish this is
through the use of a tokamak device.
 Electromagnets are
used to confined the
plasma.
 Other approaches
use:
 laser beams to
increase pressure;
 pulsed-power to
“Z-pinch” a small
pellet.
65