Atoms and Nuclei

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Atoms and Nuclei

• Professor Jasmina Vujic
• Lecture 1
• Nuclear Engineering 162
• Department of Nuclear Engineering
• University of California, Berkeley

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ATOMS AND NUCLEI

• ATOMS Greek indivisible the smallest parts
  of matter that retain their physical and chemical
  properties

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INSIDE THE ATOM

• The center consists of a heavy NUCLEUS with a
  POSITIVE electric charge, which is surrounded by
  a swarm of much lighter particles, the NEGATIVELY
  charged ELECTRONS.

A crude approximation of the hydrogen atom is a
MARBLE (the nucleus) in the center of a FOOTBALL
STATIUM and PINHEAD (the electron) orbiting over
the benches.
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• The NUCLEUS consists of NUCLEONS with are of two
  types
• PROTONS, with a positive charge
• NEUTRONS, which have no electric charge

In a free atom, the number of electrons EQUALS
the number of protons, and the atom is
electrically NEUTRAL.
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ELEMENTS

• There are more than 120 chemical ELEMENTS (92
  elements present in nature).
• ATOMIC NUMBER, Z. All atoms of a given element
  have the same number of protons (electrons),
  which is called the atomic number.
• MASS NUMBER, A. The total number of nucleons
  (protons and neutrons) inside the nucleus is
  called the atomic mass number.

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ISOTOPES

• The nuclei with the same number of protons and
  different number of neutrons are called ISOTOPES.
  They pertain to the same element, they have the
  same chemical properties, but different physical
  properties (different mass numbers)

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• ATOMIC MASS, M. The mass in grams of 6.02x1023
  atoms.
• M 1.008 g for hydrogen,
• M 4.003 g for helium,
• M 16.00 g for oxygen,
• M 238.0 g for uranium

AVOGADROS Number, Nav 6.022142x1023
atoms/mole
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The Atomic Mass Unit
Is defined to be 1/12 the mass of a neutral
ground-state atom of 12C

• Avogadros number (Nav) 6.022142x1023
  molecules/mole
• 1 gram mole (12C) 12.0000 g/mole

The mass of one (12C) atom (12.0000 g/mole)/ Nav
1.9926x10-23 g
1 amu 1.9926x10-23 g/12 1 amu 1.660538x10-24
g
The energy equivalent of 1 amu E(1 amu)
931.494 MeV
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The Atomic Mass Unit

• NUMBER DENSITY, N. Number of atom per cubic
  centimeter.
• EXAMPLE
• Uranium with mass density of 19 g/cm3, has the
  number density of

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Energy and Matter

• The equivalence of MATTER and ENERGY
• Einsteins Formula
• E mc2
• The speed of light,
• c 3108 m/s
• Matter can be converted into ENERGY, and ENERGY
  can be converted into MATTER
• Conversion of 1 kg of matter into energy
  releases
• E mc2 (1 kg)(3108 m/s)2 91016 J

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Conversion of Energy and Matter

• Proton rest mass
• 1.672 621 610-27 kg or 938.272 MeV
• 1.007 276 amu
• Neutron rest mass
• 1.674 927 210-27 kg or 939.565 MeV
• 1.008 664 amu
• Electron rest mass
• 9.109 381 9 10-31 kg or 0.511 MeV

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Conversion of Energy and Matter

• In burning of 1 kg of uranium, 0.87 g of matter
  is converted into energy
• EU(0.87)(91016 J)7.81013 J
• Combustion of 1 kg of gasoline releases
• Eg5107 J
• The energy yield from one kilogram of uranium is
  more than a MILLION times that from fossil fuel.

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Models of Atom

• Thomsons plum pudding model
• Rutherfords model - the first planetary model
• Bohrs model
• Paulis exclusion principle (1925)

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Thomson The Plum Pudding Model

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The Rutherford Atomic Model - 1911

• 1900 Alpha, beta and gamma rays were discovered
• 1909 Rutherford bombarded thin gold foils with
  alpha particles (Po(214-84))
• Large angle deflection seen in 1/8000 alpha
  particles suggests the existence of a very small
  and massive nucleus
• Proposed the planetary model
• We now know
• Rnuc 1.3 A1/3 x 10-15 m
• Ratom 1.5 x 10-10 m

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Bohrs hydrogen atom - 1913

• Bohr was not satisfied with the Rutherfords
  model -
• classical mechanics did not work for the
  planetary model - it violated classical laws of
  electromagnetism
• Unstable model, since an accelerated charge will
  emit light and therefore lose E -
• Bohr postulates the first semi-classical model
• Angular momentum of electron is quantized
• mvr nh
• Then energy and orbital radii are also quantized
  (derive radius on the board)
• rn 0.529 n2/Z (Å)
• En -13.6 Z2/n2 (eV)

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Bohrs Atomic Model

• The orbital electrons can revolve around the
  nucleus only in certain
• fixed radii, called stationary states such that
  the angular momentum of
• electrons must be integral multiplies of h/2p
• mvr n(h/2p)

where n is the principal quantum number
h is Planks constant
A photon is emitted only when an electron falls
from one orbit to another orbit of lower energy.
The energy of photon is equal to the difference
between the energy levels on the electron in the
two orbits
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Bohrs Atomic Model

• The normal condition of the atom, or ground
  state, is the state with n1. The atom is in
  its lowest possible energy state and its most
  stable condition.

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Energy Levels of the Hydrogen Atom
Ionization Continuum
0 eV
N4
N3
N2
Balmer Series visible
-13.6 eV
N1
Lyman Series (ultraviolet)
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Bohrs Atomic Model

• Excitation of the Atom
• When a sufficient amount of energy is transferred
  to the atom, causing an electron to jump from
  the lower to higher energy levels, the atom is
  said to be excited.
• Ionization of the Atom
• When a sufficient amount of energy is transferred
  to the atom, causing an electron to be removed
  from the electric field of the nucleus, the is
  said to be ionized, and the negative electron
  together with the remaining positively charged
  atom, is called the ion pair.
• Excitation and ionization are the main mechanisms
  through which energy is transferred from
  radiation to matter

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Problem with Bohrs model and classical mechanics

• Could only predict correctly the energy levels of
  H.
• The dual behavior of light (particle and wave)
  could not be explained by classical mechanics
• The approach of Bohr of mixing classical mechanic
  with quantizing certain variables was suddenly
  heavily used
• other accurate predictions were made with new
  semi-classical or relativistic models
• Prelude to Quantum Mechanics

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Periodic Table of Elements and the Pauli
Exclusion Principle

• To describe an atom completely, it is necessary
  to specify four quantum numbers, for each of the
  orbital electrons
• n Principal quantum number 1,2,3...
• l Azimuthal quantum number 0 to (n-1)
• m Magnetic quantum number -1 to 0 to 1
• s Spin quantum number 1/2

The Pauli Exclusion Principle no two electron in
any atom may have the same set of four quantum
numbers
N 2n2
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Pauli principle No two electrons in an atom can
be in the same state

• Quantization came naturally out of quantum
  mechanics
• Four quantum numbers fully described the electron
  energy levels
• Principal quantum number n
• Describes the orbital shells
• n1, 2 and 3 for K, L and M shells respectively
• Corresponds to Bohrs angular momentum
  quantization
• Azimuthal quantum number l
• Explains fine structure in spectrum (elliptic
  orbit)
• l 0, 1, 2, , n
• Magnetic quantum number m
• Explains splitting of spectral lines in magnetic
  field - Zeeman Effect
• m -l, l
• Intrinsic spin (angular momentum) of electron s
• s -1/2, ½

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Binding Energy

• The nucleons (protons and neutrons) are bound
  together by a net force which NUCLEAR ATTRACTION
  forces exceed the ELECTROSTATIC (COULOMB)
  REPULSION forces. Associated with the net force
  is a POTENTIAL ENERGY of BINDING.
• In order to separate the nucleus into its
  component nucleons, energy must be supplied from
  the outside.
• Binding Energy(B)total mass of separate
  particles - mass of the atom

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Binding Energy
This is average binding energy per nucleon
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Binding Energy

• Why energy is released in FISSION and FUSION
  processes?

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Binding energy
Lets revisit the fusion of four protons to form
a 4He nucleus
these masses come from the table of nuclides
We have calculated the mass deficit --gt i.e. the
whole is less than sum of the parts The mass
deficit is represented by a HUGE energy release,
which can be calculated using Einsteins famous
equation, Emc2, and is usually expressed in Mev
56Fe
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Contributions to Binding Energy
EB strong nuclear force binding -surface
tension binding spin pairing shell
binding-Coulomb repulsion
1) strong nuclear force -- the more nucleons the
better 2) surface tension -- the less
surface/volume the better (U better than He) 3)
spin pairing -- neutrons and protons have and -
spins, paired spins better 4) shell binding --
nucleus has quantized shells which prefer to be
filled (magic numbers) 5) Coulomb repulsion --
packing more protons into nucleus comes at a cost
(although neutron addition will stabilize high Z
nuclei)
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Binding Energy

• Liquid Drop Model (Explains fission)
• The nucleus is thought to be a homogenous mixture
  of nucleons in which all the nucleons interact
  strongly with each other.
• Shell Model (Explains radioactive decay)
• The various nucleons exist in certain energy
  levels within the nucleus, and interact weakly
  among themselves.
• So-called magic numbers have been found,2,8, 20,
  50, 82, 126- isotopes containing these number of
  protons or neutrons have unusual stability in
  their structure.
• Nucleons can be excited to higher energy levels.
  Gamma rays emitted.

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