Chapter 7: The Nucleus Part 1

1
Chapter 7 The Nucleus Part 1

• Alyssa Jean-Mary

2
The Atom

• Atoms are the smallest particles of ordinary
  matter
• An atom contains protons, neutrons, and electrons
• The protons and neutrons are located in the
  central core of the atom, which is called the
  nucleus
• The electrons move around the nucleus
• The protons and neutrons provide almost all of
  the atoms mass since the electrons are much
  lighter than them
• There is the same number of electrons and
  protons, which makes the atom electrically
  neutral, since electrons have a negative charge
  and protons have a positive charge
• Almost all the energy that is available to us has
  a nuclear origin
• The sun gets its energy from nuclear reactions
  and transformations, and coal, oil, natural gas,
  wind, and falling water get all their energy from
  the sun
• The heat in the interior of the earth is due to
  nuclear processes
• Nuclear reactors produce energy using nuclear
  processes

3
Rutherford Model of the Atom

• In 1911, British physicist Ernest Rutherford
  provided an experiment to determine what is
  inside an atom
• Before this, all that was known is that atoms
  exist, and that they contain electrons. Also,
  since an atom is neutral and electrons carry a
  negative charge, there has to be some type of
  positively charged matter inside atoms.
• In Rutherfords experiment, alpha particles were
  used as probes. Alpha particles are about 8000
  times heavier than an electron, and they have a
  positive 2 charge. A substance that emits alpha
  particles was placed behind a lead screen that
  had a small hole in it. Thus, a narrow beam of
  alpha particles was produced. This beam was aimed
  at a thin gold foil. On the other side of the
  foil was a zinc sulfide screen. A zinc sulfide
  screen gives off a visible flash of light when it
  is struck by an alpha particle.
• What was expected by Rutherford in this
  experiment was that the alpha particles would go
  right through the foil with hardly any
  deflection, since it was assumed that the
  electric charge in an atom was uniformly spread
  throughout its volume. If only weak electric
  forces are thus exerted on alpha particles, they
  should pass through the foil and only be
  deflected 1 or less.
• What was actually found that, although most of
  the alpha particles followed what Rutherford
  expected (i.e. that they werent deflected much),
  a few of them were scattered through very large
  angles, some of them even being scattered in the
  backward direction.

4
The Nucleus is Small

• Since alpha particles are relatively heavy, and,
  in Rutherfords experiment, they were traveling
  at high speeds, there must be a strong force that
  is exerted on them for some of them to have such
  a great amount of deflection.
• The only way Rutherford could explain this was
  that an atom has a tiny nucleus, where all the
  positive charge and nearly all the mass of the
  atom is contained, and electrons that are some
  distance away from this nucleus.
• Since in his explanation, an atom is largely
  empty space, it accounts for most of the alpha
  particles passing right through the thin foil
  without being strongly deflected. Also, even if
  an alpha particle happened to encounter an
  electron, since an electron is so light, it would
  have little effect on the alpha particle. It also
  accounts for those alpha particles that were
  strongly deflected. These alpha particles came
  near the nucleus, and they are deflected through
  a large angle since there is a strong electric
  field present near the nucleus.
• Thus, Rutherfords experiment showed that
  ordinary matter is mostly empty space. All
  ordinary matter is just a collection of electric
  charges that are very far away from each other.
  If all the electrons and nuclei in our bodies
  were packed closely together, we would be no
  larger than specks that are just visible with a
  microscope.

5
The Structure of the Nucleus

• A nucleus, except for the simplest nucleus, that
  of a hydrogen atom, which usually contains only
  one proton, consists of two particles the proton
  and the neutron
• The proton has a positive charge and a mass that
  is 1836 times greater than the mass of the
  electron
• The neutron has no charge and a mass that is 1839
  times greater than the mass of the electron and
  thus, only slightly larger than the mass of the
  proton
• In the matter all around us, elements are the
  simplest substances contained within it
• Over 100 elements are known at room temperature
  and atmospheric pressure, 11 of these are gases,
  including hydrogen, helium, oxygen, chlorine, and
  neon, 2 (bromine and mercury) are liquids, and
  the rest are solids
• In a neutral atom of an element, the number of
  protons is the same as the number of electrons.
  This number is called the atomic number of the
  element. The atomic number of an element is its
  most basic property. This is because the atomic
  number of an element determines how many
  electrons are present and how these electrons are
  arranged, which governs the physical and chemical
  behavior of the element. The periodic table gives
  the atomic numbers and symbols of all the
  elements.

6
The Periodic Table
7
Isotopes

• All atoms of an element have the same number of
  protons, but not always the same number of
  neutrons
• For example, most hydrogen atoms (99.9) have
  only one proton and no neutrons, but a few have
  one proton and one neutron and even less have one
  proton and two neutrons
• Isotopes of an element contain the same number of
  protons, but different numbers of neutrons. All
  elements have isotopes.
• A nucleus that has a particular composition is
  called a nuclide. The nuclide symbol is
• AZX
• where X is the symbol of the element, Z is the
  atomic number of the element, which is also the
  number of protons in the nucleus, and A is the
  mass number, which is the number of protons plus
  the number of neutrons in the nucleus
• For example, if an isotope of chlorine has 17
  protons and 18 neutrons, the atomic number, Z,
  equals 17, and the mass number, A, equals 17
  18, which is 35. Thus, the nuclide symbol is
  3517Cl. This nuclide symbol can be shortened to
  35Cl or Cl-35.
• Nucleon refers to both protons and neutrons.
  Thus, the mass number, A, is the number of
  nucleons in the nucleus

8
Radioactivity

• In Paris, in 1896, Henri Becquerel accidentally
  discovered that uranium, an element, can
• expose covered photographic film
• ionize gases
• cause certain materials, such as zinc sulfide, to
  glow in the dark
• From this, Becquerel concluded that uranium gives
  off some kind of invisible but penetrating
  radiation, which is a property called
  radioactivity.
• When Pierre and Marie Curie were extracting
  uranium in the same laboratory, they found two
  other elements that were also radioactive. One
  was named polonium, after Poland, where Marie
  Curie was from, and the other one was named
  radium, which is thousands of times more
  radioactive than uranium
• The ability of a radioactive material to emit
  radiation is not changed by chemical reactions,
  by heating it in an electric arc, or by cooling
  it in liquid air. Thus, radioactivity is
  associated with the nucleus of an atom, because
  this is the only part of an atom that is
  unaffected by these treatments.
• The radioactivity of an element is due to the
  radioactivity of one or more of its isotopes. In
  nature, most elements dont have any radioactive
  isotopes. These can be prepared artificially,
  however, and are useful as tracers in
  biological and medical research. In this
  research, a radionuclide is incorporated into a
  chemical compound. A researcher can follow what
  happens to this compound in a living organism by
  monitoring the radiation from the isotope. Some
  elements have some stable isotopes and some
  radioactive ones, but other elements, like
  uranium, have only radioactive isotopes.
• Of the approximant 7000 nuclides that might
  exist, 2000 have either been found in nature or
  created in a laboratory. Of these 2000, only 256
  are stable, and thus do not undergo radioactive
  decay.

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Radioactive Decay

• A magnetic field splits the radiation from a
  radioactive material into three parts
• One part is deflected as though it consists of
  positively charged particles. This part is called
  alpha particles. Alpha particles are the nuclei
  of helium atoms (i.e. helium atoms without their
  electrons), so they contain two protons and two
  neutrons, and their symbol is 42He. Alpha
  particles are the least penetrating of the three.
• Another part is deflected as though it consists
  of negatively charged particles. This part is
  called beta particles. Beta particles are
  electrons.
• The rest is not deflected because they are not
  affected by the magnetic field. These are the
  gamma rays. Gamma rays are electromagnetic waves
  with frequencies that are higher than x-rays. A
  gamma ray is emitted by a nucleus when it has
  more than its normal amount of energy. When it is
  emitted, the composition of the nucleus does not
  change, unlike when alpha particles or beta
  particles are emitted. Gamma rays are the most
  penetrating of the three kinds of radiation.

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Why Radioactive Decay Occurs

• A nucleus decays when it emits one of the three
  kinds of radiation (i.e. an alpha particle, a
  beta particle, or a gamma ray)
• Alpha decay (i.e. when an alpha particle is
  emitted) occurs when a nucleus is too large to be
  stable. Since the forces that hold protons and
  neutrons together in a nucleus only act over
  short distances, they only interact strongly with
  their nearest neighbors. Because the electrical
  repulsion of the protons (i.e. protons repel
  protons because like charges repel) is strong
  throughout the entire nucleus, there is a limit
  to the ability of the neutrons to hold a large
  nucleus together. The bismuth isotope, 20983Bi,
  is the heaviest, stable (i.e. not radioactive)
  nucleus. All nuclei that undergo alpha decay
  become smaller.
• Another cause of radioactive decay is when the
  ratio of neutrons to protons is too large or too
  small. A small nucleus is stable when the number
  of protons and neutrons are the same. In a large
  nucleus, however, more neutrons than protons are
  needed in order to overcome the electrical
  repulsion of the protons.
• Beta decay occurs when a nucleus has too many
  neutrons. Here, one of the neutrons spontaneously
  turns into a proton, which causes the emission of
  an electron.
• When a nucleus has too few neutrons to be stable,
  one of the protons can become a neutron, which
  causes the emission of a positron. A positron is
  an electron that has a positive charge instead of
  a negative charge. Another way to form a neutron
  in a nucleus that has too few neutrons is to have
  one of the electrons absorbed by one of the
  protons, which is called electron capture.
• Some nuclide require a number of radioactive
  decays before they reach a stable form.
• For instance, the uranium isotope, 23892U,
  undergoes eight alpha decays and six beta decays
  before it becomes the stable, nonradioactive lead
  isotope, 20682Pb.

11
Neutrons and Protons Outside the Nucleus

• Any neutron that is outside the nucleus is
  unstable, and thus undergoes radioactive decay
  into a proton and an electron. But, do not think
  of a neutron as a combination of a proton and an
  electron a neutron is a separate particle that
  has its own unique properties. If we try to
  create a neutron by bringing a proton and an
  electron together, what we would get would be a
  hydrogen atom, not a neutron.
• Any proton that is outside the nucleus is stable.

12
Half-Life

• The half-life of a radionuclide is the period of
  time needed for half of the initial amount of the
  nuclide to decay. Thus, as time goes on, the
  amount of the nuclide that is not decayed becomes
  smaller and smaller, but there is always still
  some left.
• For example, the radium isotope, 22688Ra, which
  alpha decays to the radon isotope, 22286Rn, has a
  half-life of 1600 years. If there is initially
  1.0mg of radium, after 1600 years, 0.5mg of
  radium remains and 0.5mg of radium has decayed
  into radon. After another 1600 years, only 0.25mg
  of radium remains. After another 1600 years, a
  total of 4800 years (i.e. 3 half-lives), only
  0.125mg of radium remains, which is still a fair
  amount. Even after 6 half-lives (i.e. 9600
  years), over 1 percent of the initial amount of
  radium still remains undecayed.
• Every radionuclide has a characteristic and
  unchanging half-life. Half-lives range from a
  millionth of a second to billions of years.
• For instance, radon, which is an alpha emitter,
  has a half-life of 3.8 days, verses radium,
  which, as stated above, has a half-life of 1600
  years.
• One of the biggest problems that nuclear power
  plants face is the safe disposal of the
  radioactive waste they produce. This is a problem
  because many isotopes used by nuclear power
  plants have long half-lives.
• Radioactive decay is used in methods that date
  archaeological specimens and rock samples, even
  including the samples that were brought back from
  the moon.

13
Radiation Hazards

• All radiation from radionuclides ionize the
  matter that they pass through. All radiation that
  ionizes matter is harmful to living tissue. If
  the damage from radiation is only slight, then
  the living tissue can often repair itself without
  any permanent effect.
• The hazards of radiation are often underestimated
  because there is usually a delay between the
  exposure to the radiation and some of the
  consequences of that exposure. This delay can be
  many years. Some of the consequences of radiation
  exposure are cancer, leukemia, and changes to the
  reproductive cells, which can lead to having
  children with physical deformities and mental
  handicaps.
• Radiation dosage is measured in sieverts (Sv).
  One Sv is the amount of radiation that has the
  same biological effects as those produced when 1
  kg of body tissue absorbs 1 joule (J) of x-rays
  or gamma rays. There is a link between radiation
  exposure and the likelihood of developing cancer,
  but radiobiologists cant agree on the exact
  relationship between the two.
• The radiation dosage per person from natural
  sources of radiation is about 3 mSv/y, which is
  averaged over the U.S. population. Since 1 mSv is
  equal to 0.001 Sv, 3 mSv is 0.003 Sv. Other
  sources of radiation (i.e. not natural) adds
  about 0.6 mSv/y. These other sources include
  medical x-rays, which contribute the largest
  amount. For example, a typical mammogram involves
  a dosage of 4 mSv. Thus, the average total per
  person from all sources of radiation is about 3.6
  mSv/y.

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Natural Sources of Radiation

• The figure shows the natural sources of radiation
  that provide the radiation dosage that is
  received by an average person in the U.S.
• The most important natural source, representing
  55, is the radioactive gas radon, which is a
  decay product of radium, which is a decay product
  of uranium. Uranium is found in many common
  rocks. Since radon is colorless and odorless, it
  is present nearly everywhere, but it is usually
  present in amounts that are too small to endanger
  health. If a house is built in an uranium-rich
  area, however, radon becomes a problem since it
  is impossible to stop radon from entering a house
  from the ground under them. Surveys have been
  done that show that millions of Americans have
  homes that have radon concentrations high enough
  to pose a definite, although small, cancer risk.
  Radon is the second greatest cause of lung
  cancer, only behind cigarette smoking. The most
  effective method to reduce radon levels in
  existing houses in uranium-rich areas seems to be
  to extract the air from underneath the house and
  disperse it into the atmosphere, even before it
  can enter the house.
• Two other natural sources are cosmic rays and
  radionuclides present in rocks and soil, which
  each represent 8. The radiation from cosmic rays
  depends on altitude, since cosmic rays are
  gradually absorbed by the atmosphere. Near sea
  level, the radiation dosage is about 0.3 mSv/y
  and at 3700m above sea level, in La Paz, Bolivia,
  it is 2 mSv/y. Astronauts actually are exposed to
  1 mSv per day when they are in orbit.
• Even the human body is a natural source of
  radiation, since it contains tiny amounts of
  radionuclides of some elements, such as potassium
  and carbon. Radionuclides in the human body
  represent 11.
• These are the natural background radiation
  sources. There are two other natural sources of
  radiation. Medical x-rays and nuclear medicine
  represents about 15, while the last 3 is from
  occupational exposures, consumer products,
  fallout from past nuclear weapons tests, and
  nuclear power plants.

15
Dose Limits

• There are many useful procedures that involve
  ionizing radiation. Some of these procedures use
  direct radiation. Two examples of these are
  x-rays and gamma rays that are used in both
  medicine and industry. Other procedures involve
  radiation that is an unwanted, but inescapable,
  byproduct, such as in the operation of nuclear
  reactors and in the disposal of their wastes.
• About 9 million people around the world get
  exposed to radiation at work. In some countries,
  the radiation dosage limit is about 20 mSv/y.
  This dosage corresponds to an estimated risk of
  fatal cancer of 1 in 1000. In the U.S., the
  radiation dosage limit is 50 mSv/y. For the
  general public, the maximum radiation dosage from
  artificial sources is 1 mSv/y, which was set
  internationally. This dosage corresponds to a
  risk of 1 in 20,000. If a person smokes 10
  cigarettes a day, their risk is 1 in 200.

16
X-rays

• There should always be a balance between risk and
  benefit from radiation. It is not always easy to
  find this balance, though. This is often a
  problem for exposure to medical x-rays. X-rays
  are sometimes taken for no strong reason, so they
  might do more harm than good.
• These no strong reason x-rays include routine
  chest x-rays when a person is admitted into a
  hospital, routine x-rays when a person is
  receiving a regular physical examination, and
  routine dental x-rays. These are particularly
  harmful for children because they are especially
  at risk for thyroid cancer.
• The routine x-rays of women without symptoms to
  search for breast cancer is actually generally
  thought to have increased, not decreased the
  overall death rate due to cancer.
• It is particularly dangerous to x-ray pregnant
  women, since this dramatically increases the
  change of cancer in their children. It was a
  routine procedure until not long ago.
• X-rays do have many valuable applications in
  medicine, however. The point is that every
  exposure to x-rays should have a definite
  justification that outweighs the risk involved.
  This is especially true for CT scans. CT scans
  usually involve radiation dosages of 8 mSv, which
  is a hundred times the radiation dosage from an
  ordinary x-ray using modern equipment.

17
Units of Mass and Energy

• Until now, for us, the unit of mass is the
  kilogram and the unit of energy is the joule.
  These units are too large to apply to the atomic
  world, so smaller units for mass and energy are
  used.
• For mass, the smaller unit is the atomic mass
  unit (u), which is equal to 1.66 x 10-27 kg. This
  is the approximate mass of the hydrogen atom,
  whose actual mass is 1.008 u.
• For energy in atomic physics, the smaller unit is
  the electronvolt (eV), which is equal to 1.60 x
  10-19 J. An electronvolt is the amount of energy
  that is gained by an electron that is accelerated
  by a potential difference of 1 volt.
• The amount of energy that is needed to remove an
  electron from an atom is one quantity that is
  expressed in electronvolts. For example, for a
  nitrogen atom, the amount of energy needed to
  remove an electron is 14.5 eV.
• For energy in nuclear physics, the smaller unit
  is the megaelectronvolt (MeV), since the
  electronvolt is too small. A megaelectronvolt
  (MeV) is equal to 106 eV or 1.69 x 10-13 J.
• The amount of energy of the radiation that is
  emitted by a radionuclide is one quantity that is
  expressed in megaelectronvolts. For example, the
  amount of energy of the alpha particle that is
  emitted by a nucleus of the radium isotope,
  22688Ra, is 4.9 MeV.
• The energy equivalent (E0 mc2) of a rest mass
  of 1 u is 931 MeV.

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Binding Energy 1

• As was shown above, the nucleus of an ordinary
  hydrogen atom only has a single proton. Its
  nuclide symbol is 11H.
• The isotope of hydrogen that is called deuterium
  has one proton and one neutron. Its nuclide
  symbol is 21H.
• What is expected is that the mass of the
  deuterium atom should equal the mass of the
  ordinary hydrogen atom, 11H, which is about
  1.0078 u, plus the mass of a neutron, which is
  about 1.0087 u. Thus, the expected mass of the
  deuterium atom is 2.0165 u. But, the measure mass
  of the deuterium atom is only 2.0141 u. This is
  0.0024 u less than the expected mass.
• All atoms, except for ordinary hydrogen, 11H,
  have less mass than the combined masses of the
  particles that they are composed of. Thus, the
  conclusion is that stable nuclei are stable
  because they lack enough mass to break up into
  separate nucleons.

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Binding Energy 2

• When a nucleus forms, a certain amount of energy
  is given off because of the action of the forces
  that hold together the neutrons and protons. This
  energy comes from the mass of the particles that
  join together. Thus, the resulting nucleus has
  less mass than the total mass of the particles
  before they are joined. The amount of energy
  given off is the amount of missing mass the atom
  has times the energy equivalent of 1 u of mass,
  931 MeV. Thus, for the deuterium atom, since the
  missing mass is 0.0024 u, the amount of energy
  given off is 0.0024 u multiplied by 931 MeV,
  which equals 2.2 MeV.
• To test these missing mass interpretations,
  experiments are performed to see how much energy
  is needed to break apart a deuterium nucleus into
  a separate neutron and proton. These experiments
  show that this amount of energy is indeed 2.2
  MeV, what we expected. If less than 2.2 MeV of
  energy is applied to a deuterium nucleus, the
  nucleus wont break apart it will stay together.
  When more than 2.2 MeV of energy is applied to a
  deuterium nucleus, the excess energy goes into
  the kinetic energy of the neutron and proton as
  they fly apart.
• The binding energy of a nucleus is the energy
  equivalent of the missing mass of the nucleus. If
  a nucleus has a greater binding energy, then more
  energy is needed to break it up.
• Nuclear binding energies are quite high. For
  stable nuclei, the range of bindinge energies is
  2.2 MeV, which is for the deuterium isotope, 21H,
  to 1640 MeV, which is for 20983Bi, an isotope of
  bismuth. All larger nuclei are unstable and
  undergo radioactive decay.
• A typical binding energy in kJ/kg is 8 x 1011
  kJ/kg, or 800 billion kJ/kg. The amount of energy
  needed to boil water is its heat of vaporization,
  which is only 2260 kJ/kg. The amount of energy
  given off by burning gasoline is only 4.7 kJ/kg,
  which is 17 million times smaller than a typical
  binding energy.