Download Chapter 26

The Nucleus


What goes on in the nucleus of an atom has
almost nothing to do with the atom’s
chemistry , and vice versa.
The energies available in the nucleus are
much greater than those available among
electrons.
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All nuclei are composed of protons and neutrons
◦ Exception is ordinary hydrogen with just a proton
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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, A, is the number of nucleons
in the nucleus
◦ A=Z+N
◦ Nucleon is a generic term used to refer to either a proton
or a neutron
◦ The mass number is not the same as the mass
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Symbol:
A
◦ X is the chemical symbol of the element
Z
 Example:
X
◦




Mass number is 27
Atomic number is 13
Contains 13 protons
Contains 14 (27 – 13) neutrons
27
The Z may be omitted since the element can be
13 to determine Z
used
Al
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The nuclei of all atoms of a particular element
must contain the same number of protons
They may contain varying numbers of
neutrons
◦ Isotopes of an element have the same Z but
differing N and A values
◦ Example:
11
6
C
12
6
C
13
6
C
14
6
C
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The proton has a single positive charge, +e
The electron has a single negative charge, -e
The neutron has no charge
◦ Makes it difficult to detect
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e = 1.602 177 33 x 10-19 C

It is convenient to use unified mass units, u,
to express masses
◦ 1 u = 1.660 559 x 10-27 kg
◦ Based on definition that the mass of one atom of
C-12 is exactly 12 u
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Mass can also be expressed in MeV/c2
◦ From ER = m c2
◦ 1 u = 931.494 MeV/c2

Since the time of
Rutherford, many
other experiments
have concluded:
◦ Most nuclei are
approximately spherical
◦ Average radius is
1
3
-15
roxA10 m
 ror=
1.2
 A is the number of
nucleons
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The volume of the nucleus (assumed to be
spherical) is directly proportional to the
total number of nucleons
This suggests that all nuclei have nearly the
same density
Nucleons combine to form a nucleus as
though they were tightly packed spheres
An atom has nine protons and eight neutrons
in the nucleus and 10 electrons in orbit.
1. What element is?
2. What is its mass number?
3. What is it’s atomic number?
4. What is its electric charge?
5. How is possible that the number of protons
and electrons is different?
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How many protons ,neutrons , and electrons
are contained in the atom 56Fe when it has a
charge of +2?
Atomic number is 26.
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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
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
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
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Mass and Energy are equivalent.
C is speed of light = 3X 108 m/s , It is a very
large number.
A given amount of mass can be converted
into energy.

The total energy of the bound system (the
nucleus) is less than the combined energy of
the separated nucleons
◦ This difference in energy is called the binding
energy of the nucleus
 It can be thought of as the amount of energy you need
to add to the nucleus to break it apart into separated
protons and neutrons
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Except for light nuclei, the binding energy
is about 8 MeV per nucleon
The curve peaks in the vicinity of A = 60
◦ Nuclei with mass numbers greater than or less
than 60 are not as strongly bound as those near
the middle of the periodic table
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The curve is slowly varying at A > 40
◦ This suggests that the nuclear force saturates
◦ A particular nucleon can interact with only a
limited number of other nucleons
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Radioactivity is the spontaneous emission of
radiation
Experiments suggested that radioactivity was
the result of the decay, or disintegration, of
unstable nuclei
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Three types of radiation can be emitted
◦ Alpha particles
 The particles are 4He nuclei
◦ Beta particles
 The particles are either electrons or positrons
 A positron is the antiparticle of the electron
 It is similar to the electron except its charge is +e
◦ Gamma rays
 The “rays” are high energy photons
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A radioactive beam is
directed into a region
with a magnetic field
The gamma particles
carry no charge and
they are not deflected
The alpha particles are
deflected upward
The beta particles are
deflected downward
◦ A positron would be
deflected upward
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Alpha particles
◦ Barely penetrate a piece of paper
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Beta particles
◦ Can penetrate a few mm of aluminum
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Gamma rays
◦ Can penetrate several cm of lead
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The decay curve
follows the equation
◦ N = No e- λt
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The half-life is also a
useful parameter
◦ The half-life is defined
as the time it takes for
half of any given
number of radioactive
nuclei to decay
T1 2 
ln 2


0.693

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The unit of activity, R, is the Curie, Ci
◦ 1 Ci = 3.7 x 1010 decays/second
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The SI unit of activity is the Becquerel, Bq
◦ 1 Bq = 1 decay / second
 Therefore, 1 Ci = 3.7 x 1010 Bq
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The most commonly used units of activity
are the mCi and the µCi
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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
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Symbolically
◦ X is called the parent
A nucleus
A 4
4
Z X
Z 2Y  2 He
◦ Y is called the daughter
nucleus
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Decay of
226
88
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Ra
226
222
86
Ra
Rn He
4
2
Half life for this decay
is 1600 years
Excess mass is
converted into kinetic
energy
Momentum of the
two particles is equal
and opposite
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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
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During beta decay, the daughter nucleus has
the same number of nucleons as the parent,
but the atomic number is changed by one
Symbolically
A
Z
X Y  e

A
Z
X Y  e

A
Z 1
A
Z 1
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The emission of the electron is from the
nucleus
◦ The nucleus contains protons and neutrons
◦ The process occurs when a neutron is transformed
into a proton and an electron
◦ Energy must be conserved
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To account for this “missing” energy, in
1930 Pauli proposed the existence of
another particle
Enrico Fermi later named this particle the
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Properties of the neutrino
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neutrino
◦ Zero electrical charge
◦ Mass much smaller than the electron, recent
experiments indicate definitely some mass
◦ Spin of ½
◦ Very weak interaction with matter
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Symbolically
A
Z
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XZA1Y  e   
A symbol
A
 the neutrino
◦  is the
for
Z X Z 1Y  e  
◦ is the symbol for the antineutrino
To summarize, in beta decay, the following pairs of
particles are emitted
◦ An electron and an antineutrino
◦ A positron and a neutrino
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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 photons are called gamma rays, very high
energy relative to light
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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
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Example of a decay sequence
◦ The first decay is a beta emission
◦ The second step is a gamma emission
12
5

B C *  e  
12
6
◦ The C* indicates
12
12 the Carbon nucleus is in an
6 C* 6 C  
excited state
◦ Gamma emission doesn’t change either A or Z
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Carbon Dating
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Smoke detectors
◦ Beta decay of 14C is used to date organic samples
◦ The ratio of 14C to 12C is used
◦ Ionization-type smoke detectors use a
radioactive source to ionize the air in a chamber
◦ A voltage and current are maintained
◦ When smoke enters the chamber, the current is
decreased and the alarm sounds
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Radon detection
◦ Radon is an inert, gaseous element associated with
the decay of radium
◦ It is present in uranium mines and in certain types
of rocks, bricks, etc that may be used in home
building
◦ May also come from the ground itself
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Classification of nuclei
◦ Unstable nuclei found in nature
 Give rise to natural radioactivity
◦ Nuclei produced in the laboratory through
nuclear reactions
 Exhibit artificial radioactivity
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Three series of natural radioactivity exist
◦ Uranium
◦ Actinium
◦ Thorium
 See table 29.2
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Series starts with
232Th
Processes through
a series of alpha
and beta decays
Ends with a stable
isotope of lead,
208Pb
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Structure of nuclei can be changed by
bombarding them with energetic particles
◦ The changes are called nuclear reactions
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As with nuclear decays, the atomic numbers
and mass numbers must balance on both
sides of the equation
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Alpha particle colliding with nitrogen:
Balancing the equation allows for the
identification
of
X
4
14
1
2
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He 
7
N  X  1H
So the reaction is
X 
4
2
He 
17
8
14
7
X 
N
17
8
O
17
8
1
1
O H
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Radiation absorbed by matter can cause
damage
The degree and type of damage depend on
many factors
◦ Type and energy of the radiation
◦ Properties of the absorbing matter
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Radiation damage in biological organisms is
primarily due to ionization effects in cells
◦ Ionization disrupts the normal functioning of the
cell
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Roentgen [R]
◦ That amount of ionizing radiation that will
produce 2.08 x 109 ion pairs in 1 cm3 of air
under standard conditions
◦ That amount of radiation that deposits 8.76 x 103 J of energy into 1 kg of air
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Rad (Radiation Absorbed Dose)
◦ That amount of radiation that deposits 10-2 J of
energy into 1 kg of absorbing material
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RBE (Relative Biological Effectiveness)
◦ The number of rad of x-radiation or gamma
radiation that produces the same biological
damage as 1 rad of the radiation being used
◦ Accounts for type of particle which the rad
itself does not
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Rem (Roentgen Equivalent in Man)
◦ Defined as the product of the dose in rad and
the RBE factor
 Dose in rem = dose in rad X RBE
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Natural sources – rocks and soil, cosmic rays
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Upper limit suggested by US government
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Occupational
◦ Background radiation
◦ About 0.13 rem/yr
◦ 0.50 rem/yr
◦ Excludes background and medical exposures
◦ 5 rem/yr for whole-body radiation
◦ Certain body parts can withstand higher levels
◦ Ingestion or inhalation is most dangerous
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Sterilization
◦ Radiation has been used to sterilize medical
equipment
◦ Used to destroy bacteria, worms and insects in food
◦ Bone, cartilage, and skin used in graphs is often
irradiated before grafting to reduce the chances of
infection
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Tracing
◦ Radioactive particles can be used to trace chemicals
participating in various reactions
 Example,
131I
to test thyroid action
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MRI
◦ Magnetic Resonance Imaging
◦ When a nucleus having a magnetic moment is
placed in an external magnetic field, its moment
processes about the magnetic field with a
frequency that is proportional to the field
◦ Transitions between energy states can be
detected electronically
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Nuclear fission is a nuclear reaction in which
a heavy nucleus (such as uranium) splits into
two lighter nuclei.
 Chain Reactions.
http://library.thinkquest.org/17940/texts/fissi
on/fission.html
 A typical fission reaction releases energy of
about 200,000,000 ev .
 Explosion of a TNT molecule releases only
30ev.
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The combined mass of the fission fragments
and neutrons produced in fission is less than
the mass of the original uranium nucleus.
The tiny amount of missing mass converted
to the awesome amount of energy.
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If a U-238 split into two identical pieces and
then each piece underwent an alpha decay ,
what would the two final pieces be?
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When two light nuclei combine to form a
heavier nucleus.
All stars generate their energy through fusion
processes.
Proton-Proton Cycle
http://hyperphysics.phyastr.gsu.edu/hbase/astro/procyc.html#c1