Nuclear Physics

1
Chapter 11

• Nuclear Physics

2
The nucleus

• The nucleus occupies the very center of the atom.
• It is tiny yet incredibly dense
• More than 99.9 of the atoms 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.

3
The nucleus, contd

• The nucleus contains two type of particles.
• The proton and neutron.
• These particles have a mass about 1,840 times the
  electron mass.

4
The nucleus, contd

• It is convenient to introduce an appropriate unit
  of mass, called the atomic mass unit, u

5
The nucleus, contd

• 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 atoms mass.
• The neutron number, N, is the number of neutrons
  contained in a nucleus.

6
The nucleus, contd

• The mass number, A, is the total number of
  protons and neutrons in a nucleus.
• We omit the electrons mass because it so small
  compared to the protons and neutrons.
• Protons and neutrons are collectively referred to
  as nucleons.

7
The nucleus, contd

• 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.

8
The nucleus, contd

• 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.

9
The nucleus, contd

• 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.

10
The nucleus, contd

• We use a special notation to represent each
  isotope.
• The elements chemical symbol is used.
• A subscript to the left of the chemical symbol
  represents the atoms atomic number Z.
• A superscript to the left of the chemical symbol
  represents the atoms atomic mass A.

Helium-4 Carbon-14
Carbon-12 Uranium-235
11
The nucleus, contd

• 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

12
The nucleus, contd

• We use a similar notation for atomic particles.
• The superscript is the mass in atomic units.
• Zero for the electron since it is so small.
• The subscript is the electric charge.

13
The nucleus, contd

• 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.

14
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.

15
Radioactivity, contd

• This diagram shows the number of neutrons
  versus the number of protons in the isotopes.
• Stable isotopes are indicated by a small square.

16
Radioactivity, contd

• There are three types of nuclear radiation
• alpha radiation (a) are made of helium nuclei.
• Two protons and two neutrons.
• Has a positive electric charge.
• beta radiation (b) are made of high energy
  electrons.
• Has a negative electric charge.
• gamma radiation (g) is EM radiation.
• Has no electric charge.

17
Radioactivity, contd

• 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.

18
Radioactivity, contd

• 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.

19
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.
• The nucleus did not contain an alpha particle.
• This is just a stable collection of particles
  that can be ejected.

20
Alpha decay, contd

• 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.

21
Alpha decay, contd

• Here is a diagram illustrating alpha decay.
• We start with an unstable plutonium nucleus.
• We obtain
• a uranium nucleus, and
• an alpha particle.

22
Alpha decay, contd

• 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.

23
ExampleExample 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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ExampleExample 11.1

• ANSWER
• The reaction is

25
Beta decay

• Beta decay occurs when an unstable nucleus ejects
  a beta particle.
• Recall that an beta particle is just an electron
• 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, contd

• 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.

27
Beta decay, contd

• 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).

28
Beta decay, contd

• 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.

29
ExampleExample 11.2

• The isotope iodine-131 undergoes beta decay.
  Write the reaction equations, and determine the
  identity of the daughter nucleus.

30
ExampleExample 11.2

• ANSWER
• The reaction is

31
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.
• The nucleus does not contain any photons.
• This decay is similar to an excited atom emitting
  a photon.

32
Gamma decay, contd

• 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.

33
Gamma decay, contd

• 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.

34
Gamma decay, contd

• 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.

35
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.

36
Applications, contd

• 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.

37
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.

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Half-life, contd

• This table shows the half-life for several
  isotopes.
• Notice that the half-lives range from
  extraordinarily short (210-21 s) to extremely
  long (4.5109 yr).

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Half-life, contd

• 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.

40
Half-life, contd

• 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.

41
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.

42
Carbon dating, contd

• 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.

43
Carbon dating, contd

• 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 half-life,
  gives information on how long ago it died.

44
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.

45
Nuclear binding energy, contd

• A convenient amount of energy is the amount of
  binding energy per nucleon.

46
Nuclear binding energy, contd

• 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.

47
Nuclear binding energy, contd

• 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.

48
Nuclear binding energy, contd

• 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.

49
Nuclear binding energy, contd

• 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.

50
Nuclear binding energy, contd

• Einstein provided the reason for this
• 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).

51
Nuclear binding energy, contd

• This difference in mass between individual
  nucleons and their combination, means we can
  liberate enormous amounts of energy.

52
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.

53
Nuclear fission, contd

• Two possible fission reactions of uranium-235 are

54
Nuclear fission, contd

• The amount of energy released during the fission
  of one U-235 nucleus is 215 million
  electron-Volts (about 3.410-11 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.

55
Nuclear fission, contd

• 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.

56
Nuclear fission, contd

• 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.

57
Nuclear fission, contd

• 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.

58
Nuclear fission, contd

• 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.

59
Nuclear fission, contd

• Second, control rods are used to limit the number
  of neutrons that can participate in the fission
  process.

60
Nuclear fusion

• Nuclear fusion is the process of combining two
  nuclei to form a larger nucleus.
• Some common reactions are

61
Nuclear fusion, contd

• Energy is released in each case because the total
  mass of the nucleons after the fusion is less
  that the total mass before.

62
Nuclear fusion, contd

• Stars obtain most of their energy from a natural
  fusion reaction in the stars interior.
• At the Suns 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.

63
Nuclear fusion, contd

• 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.

64
Nuclear fusion, contd

• 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.

65
Nuclear fusion, contd

• 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.