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Atomic and Nuclear Structure
George Starkschall, Ph.D.
Lecture Objectives
• Describe the atom using the Bohr model
• Identify the various electronic shells and
their quantum numbers
• Recall the relationship between binding
energy and atomic properties
• Describe the production of characteristic
x-rays and Auger electrons
Lecture Objectives
• Describe the structure of the nucleus
• Calculate nuclear binding energies
• Identify factors affecting nuclear
stability
1
Bohr model (1913)
• Nucleus contains positive charge and
most of mass
– Diameter around 10-12 cm
• Electrons surround nucleus and revolve
around nucleus
– Planetary model
• Equal numbers of protons and electrons
– Net charge of zero
Bohr model (1913)
Bohr model (1913)
• Two problems: According to
classical physics
– Electrons in orbits should repel each
other making atom unstable, and
– Electrons in circular orbits should
radiate energy and spiral into nucleus
2
Bohr model (1913)
• Two postulates:
– Electrons revolve in specified orbits
with fixed radii
– Electrons gain or lose energy only when
they jump from one orbit to another
Bohr model (1913)
• Orbits labeled with numbers – quantum
numbers
– Energy gain (or loss) given by
Properties of electron
• Charge = -1.6  10-19 coulomb
• Mass = 9.1  10-31 kg
– Choose electron charge as practical unit
of charge – set electron charge to -1
3
Electronic energy levels
• Bohr theory gives specified orbits
– n is index of quantized orbit – principal
quantum number
– n = 1,2,3,…
• Given n we can calculate radius of
orbit and energy of orbit
• n identifies shell of atom
Electronic energy levels
• How to fill electron shells:
– General principle: Any system tries to
seek the lowest total energy state.
– Zero energy – electron infinitely far from
nucleus
– Energy of electron in orbit is negative
– Lowest energy is innermost orbit
– Maximum number of electrons in shell =
2n2
Electronic energy levels
4
Electronic energy sublevels
• 3 additional quantum numbers
– Azimuthal quantum number (ℓ) – eccentricity
of orbit
• ℓ = 0,1,…,n-1
– Magnetic quantum number (m) – orientation in
magnetic field
m = -ℓ,…,0,…,+ℓ
– Spin quantum number (s) – intrinsic electron
property
s = ½
Pauli Exclusion Principle
• No two electrons can have the same
set of quantum numbers.
Binding energy (Eb)
• Energy required to remove electron
completely from atom
• Normally Eb < 0 – energy must be
supplied
5
Binding energy (Eb)
Eb(eV)
n
shell
hydrogen tungsten
1
K
-13.50
-69,500
2
L
-3.40
-11,280
3
M
-1.50
-2,810
4
N
-0.90
-588
5
O
-0.54
-73
Note dependence of binding energy on n,
size of nucleus
Binding energy (Eb)
• Dependence on n
– Closer electron is to nucleus, stronger the
attractive force from nucleus
– Closer electron is to nucleus, less shielding of
nuclear charge by other electrons
• Dependence on Z
– Greater the number of protons in nucleus,
stronger the attractive force from nucleus
Electron transitions
• Photon or electron interacting with
inner shell electron gives it enough
energy to remove it from atom
– Leaves vacancy called “hole”
– Probability of producing a hole is
probability of interaction occurring
6
Electron transitions
• Outer shell electron moves into inner
shell vacancy – loss of energy
– Energy given off as radiation –
characteristic radiation
– Energy used to eject another electron –
Auger electron
Valence electrons
• Electrons in outermost shell
• No more than 8 electrons in
outermost shell
• Valence electrons determine
chemical properties of elements
• Explain periodic table – periodicity of
like chemical behavior
Nuclear structure
• Nucleus composed of protons and
neutrons – nucleons
– mass = 1.6  10-27 kg for both protons
and neutrons
– charge = +1.6  10-19 C for proton
no charge for neutron
• Note that proton charge same as
electron charge but of opposite sign
7
Mass number – atomic number
• Mass number (A) -- number of nucleons
(protons + neutrons) in nucleus
– Gives some indication of mass of
nucleus
• Atomic number (Z) -- number of protons in
nucleus and number of electrons in
neutral atom
• Neutron number (N) -- number of neutrons
in nucleus
relationship: A = Z + N
Atomic mass unit
• Unit of mass – atomic mass unit
(amu) defined as mass of carbon
nucleus with 6 protons and 6
neutrons
1 amu = 1.6605 10-27 kg
(Note: Some sources say carbon
atom, rather than nucleus.)
Atomic mass unit
• Masses:
electron
proton
neutron
= 0.00055 amu
= 1.00727 amu
= 1.00866 amu
8
Models of nuclear
structures
• Liquid drop model (Bohr) – Nucleus
composed of closely-packed
nucleons
• Shell model (Mayer) –Discrete energy
levels in nucleus
– Analogous to electron shells as
evidenced by stability of Z =2, 8, 20, 82,
126, suggesting filled nuclear shells
n/p ratio used as measure of
stability
Stability of nuclei
• Nuclei with even numbers of protons or
neutrons are more stable than those with odd
numbers
– Pairing of nuclear spins gives rise to lower energy
# of protons
# of neutrons
# stable isotopes
Even
Even
165
Even
Odd
57
Odd
Even
53
Odd
Odd
6
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Indicators of stability
• “Magic numbers”
– 2,8,20,28,50,82,126 – filled shells
• “Line of stability”
– N = Z for low Z
• Even vs odd
– Even more stable than odd
Nuclear force
• Protons should repel each other in
nucleus due to electrostatic
repulsion
• Require short range force to hold
nucleus together
– Short range force is approximately 100
times stronger than electromagnetic
force
Nuclear binding energy
• Mass of nucleus is less than sum of masses of
nucleons in nucleus -- mass defect
– Mass defect represents energy in binding
nucleons according to Einstein formula
E=mc2
– Generally express masses in terms of rest
energies:
1 amu = 931 MeV
– In these units 1 electron mass = 0.511 MeV
10
Example
Mass of 6 protons = 6 x 1.00727 amu
= 6.04362 amu
Mass of 6 neutrons = 6 x 1.00866 amu
= 6.05196 amu
Mass of 12 nucleons of 12C
= 12.09558 amu
Example
Mass of 12 nucleons of 12C
= 12.09558 amu
12
Mass of C nucleus
= 12.00000 amu
Mass defect
= 0.09558 amu
Example
Binding energy of 12C nucleus
= 0.09558 amu x 931 MeV/amu
= 89.0 MeV
Average binding energy/nucleon
= 89.0 MeV/12 nucleons
= 7.42 MeV/nucleon
11
Plot binding energy/nucleon
vs mass number
• Note low values for
small A, rising to
maximum in range
A = 60-80, then
gradually
decreasing
Nuclear fission
• Splitting of high A nucleus after
absorbing slow neutron
235U
+ slow neutron  92Kr + 141Ba + 3n +
energy
• Energy released approximately 200
MeV per fission
Nuclear fission
• Neutrons produced can cause fission
in other U nuclei giving rise to chain
reaction
– Uncontrolled chain reaction – atomic
bomb
– Controlled chain reaction – nuclear
reactor
– Chain controlled by absorbing some of
the neutrons produced in fission
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Nomenclature
• Isotope – same Z, different N
– 12C, 14C
• Isotone – same N, different Z
– 3H, 4He
• Isobar – same A, different Z,N
– 18O, 18F
• Isomer – same Z,N, different nuclear
energy states
– 99Tc, 99mTc
13