Ionising Radiation and Nuclear Reactions

Last updated Jun 29, 2023 Edit Source

# ← Physics Home

• Isotopes are variations of an element with different numbers of neutrons
  • They have the same number of protons and the same chemical properties
  • However, due to their mass numbers being different, they have different physical properties
• Some isotopes nuclei are unstable leading to them undergoing some form of decay in order to become more stable
  • These unstable atoms are known as radioisotopes and are radioactive
    • e.g. carbon-14 is a naturally occurring isotope of carbon that is unstable and undergoes radioactive decay to form nitrogen-14

• When a radioisotope undergoes radioactive decay, it will emit a high-energy particle or wave (radiation), there are several types of particles/waves emitted during radioactive decay:
  • Alpha Particles - $\alpha$
    • ${4\atop2}\alpha$ → an alpha particle is a helium nucleus (2 protons, 2 neutrons)
    • Parent atom loses two protons and two neutrons during alpha decay
      • Atomic number decreases by 2, mass number decreases by 4
    • Alpha particles have very low penetrating power
      • Can be stopped by paper (therefore it can’t penetrate the body)
    • Highly ionising
      • Can be very dangerous if alpha particles are emitted within the body
        • Interesting case where a spy was assassinated by poisoning them with a sample of a radioisotope in their drink that underwent alpha decay in his stomach in early 2000s
    • Fast as 10% of the speed of light
  • Beta Particles - $\beta$
    • ${0\atop-1}\beta$ → a beta particle is an electron
    • Parent atom turns a neutron into a proton and electron, releasing the electron
      • Atomic number increases by 1, mass number does not change
    • Beta particles have medium penetrating power
      • Can be stopped by metal
    • Weakly ionising
    • Fast as 90% of the speed of light
  • Beta+ Particles - $\beta^+$
    • ${0\atop+1}\beta$ → a positively charged beta particle is a positron
      • Has the same properties as electrons, but is positively charged
      • Positrons are a form of antimatter
    • Parent atom turns a proton turns into a neutron, positron and a neutrino $(v)$ and the positron and neutrino are emitted
      • Atomic number decreases by 1, mass number does not change
  • Gamma Waves - $\gamma$
    • ${0\atop0}\gamma$ → gamma radiation is an electromagnetic wave with a very high frequency and small wavelength
    • Parent atom transitions from an excited state to a base state
      • Atom is unchanged
    • Gamma waves have very high penetrating power
      • Can be stopped by thick lead, penetrates everything else
    • Very weakly ionising
    • Fast as light
• Nuclear equations must always show mass number, atomic number and chemical symbol for all components

• Textbook: Pearson

• Fission is the process in which an atom is split by a neutron into smaller atoms

  • Model Equation: ${x \atop y}A_p + {0\atop1}n → {x_1 \atop y_1}A_1 + {x_2 \atop y_2}A_2 + 2{0\atop1}n + {0\atop0}\gamma$
    • $x_1 + x_2 = x,\\ \\ y_1 + y_2 = y$
  • When a large nuclei is bombarded by a neutron, it usually causes it to become unstable which leads to it splitting into smaller fragments
  • A fission reaction can emit 2 or 3 neutrons
  • There can be more than two products however the combined mass and atomic number will still equal the parent atom’s mass and atomic number
  • Certain terms are used to describe nuclei in reference to fission:
    • Fissionable refers to nuclide which can undergo fission
    • Fissile refers to nuclides which will readily undergo fission
      • e.g. $U^{235},\\ U^{238},\\ Pu^{239},\\ Th^{232}$
      • There are only a small number of fissile elements
  • Chain Reaction: The products of 1 fission reaction acts as the successful reactant in further fission reactions ChainReaction
    • 3 ways to avoid a bomb:
      1. Concentration of fissile material
         • Percentage of isotope $U^{235}$ in uranium in uranium:
           • naturally ~ 0.7%
           • power station ~ 4%
           • bomb ~ 90%
      2. Amount of fuel
      3. Shape of fuel

• Fusion is the process in which two or more atoms are combined into a larger atom

  • Model Equation: ${x_1 \atop y_1}A_1 + {x_2 \atop y_2}A_2 → {x \atop y}A_r$
    • $x_1 + x_2 = x,\\ \\ y_1 + y_2 = y$
  • The resultant atom will have the combine mass and atomic number of all the components

• # Three Challenges for Thermal Nuclear Reactors:

  1. Neutrons emitted by uranium-235 (fuel) are very fast but uranium-235 is most fissile when irradiated by slow-moving neutrons
     • The emitted neutrons need to be slowed down to continue an efficient chain reaction
  2. Uranium-235 fission emits an average of 2.47 neutrons which need to be controlled as it could cause an explosion
  3. The heat generated in the reactor from the fission needs to be collected for electricity generation

Uranium-235

Uranium-235 is a readily fissile isotope of uranium. The more common isotope of uranium, $U^{238}$, is not fissile and makes up over 99% of naturally found uranium. This means naturally found uranium does not have enough uranium-235 to undergo chain-reactions.

Due to how low of a proportion uranium-235 makes up of natural uranium, uranium must be enriched with uranium-235 to be used as a fuel source. The different isotopes can be separated due to their difference in mass, however, the process of enriching uranium is very difficult and expensive

• Fuel Rods

  • Fuel rods are long, thin rods the contain pellets of enriched uranium

  • The fuel rods need to be able to sustain their own chain reaction

  • Fuel rods use uranium with 4% uranium-235

    • The enriched uranium (in pellet form) is packed into a thin aluminium tube 3-5 metres long

    300

  • A large nuclear reactor has over 1000 fuel rods in its core

    • Fuel rods need to be replaced around every 4 years

Uranium-238 → Plutonium-239

While uranium-238 is not readily fissile, it is classified as ‘fertile’ because it can form plutonium-239 after capturing a fast neutron, a product of uranium-235 fission. Plutonium-239 is readily fissile and releases similar energy to uranium-235 allowing it to sustain the chain reaction.

• Moderator
  • A material that slows down the neutrons (easier to be captured by nuclides)
    • e.g. water, heavy water, graphite, carbon dioxide
      • Heavy water is the most effective moderator but is also the most expensive
      • Water is the cheapest but absorbs a lot of neutrons reducing the extent of the chain reaction
• Control Rods
  • A nuclear reactor can also produce great amounts of energy but the energy release must be controlled
    • This is achieved by controlling the number of neutrons that are involved in the fission chain reaction
  • Control rods are material that absorbs excess neutrons
    • e.g. cadmium, boron steel
      • When a neutron strikes a control rod, it is absorbed into the nucleus of the material
• Coolant
  • The core of a nuclear reactor can reach very high temperature (500-1500$\degree$C)
  • The coolant is a liquid that run through pipes to absorb heat energy that has been produced from the core
    • e.g. water, heavy liquid, carbon dioxide, liquid sodium
• Heat Exchanger
  • A heat exchanger transfers the heat created in the reactor into pipes containing water
    • This water is converted into high-pressure steam that is used to rotate the turbines that drive the generator
• Radiation Shield
  • The radiation shield protects workers and the surrounding environment from exposure to radiation leaks from the core of the reactor
    • e.g. lead, concrete, graphite

• Low Level Waste
  • e.g. protective clothing, wrappings, containers of isotopes
  • Processed by incineration, burying and flushing
• Medium Level Waste
  • e.g. reactor component, chemical sludge
  • Processed by solidifying in concrete or burying
• High Level Waste
  • e.g. spent rods, liquid waste
  • Processed by coolant ponds or kept in secure storage
    • Spent fuel rods can be repurposed into new fuel, however the process is very expensive
  • High-level waste must be stored permanently due to how long the half-lives are for the radioactive materials

• The mass of any given nuclide is less than the sum of the individual masses of the protons and neutrons of which it is composed
  • i.e. there is a mass defect
• The mass defect is the difference between the expected total mass of a nucleus (mass of nucleons) and the actual total mass recorded (mass of nucleus)
  • Mass Defect = Mass of Nucleons - Mass of Nucleus
• The reason that the total mass is less than the expected mass is due to some mass becoming converted to nuclear binding energy which is lost in order for the nucleus to hold together
  • Energy and mass are interchangeable through the equation $E = mc^2$
  • The nuclear binding energy is not responsible for holding the nucleus together
• The nuclear binding energy is the energy equivalent of the mass lost during nucleosynthesis
  • The nuclear binding energy is the energy that would have to be added to the nucleus to restore the mass defect
• The more nuclear binding energy per nucleon, the more stable the nuclei
  • Iron-56 has the most stable nuclei

• Proton: $1.007276$
• Neutron: $1.008665$
• $1\\ u$ = one unified atomic mass unit

# Conversion Formulas: (From Formula Sheet)

• $1\\ u = 1.66 \\ ×\\ 10^{-27}$kg (mass-to-mass)
• $1\\ u =931\\ MeV$ (mass-to energy)
• $1\\ eV = 1.60\\ ×\\ 10^{-19}J$ (energy-to-energy)
  • $1\\ eV\\ ×\\ 10^{-6} = 1\\ MeV$
  • $1\\ MeV = 1,000,000\\ eV$

• Radioisotopes decay sporadically and thus can be difficult to measure the decay rate by normal means
• Instead, radioactive decay is measured in half-lives
  • A half-life is the amount of time it takes for half of the radionuclides in a sample of a given radioisotope to decay
• Half-life is graphed using an exponential graph measuring the count rate (radiation) over time HalfLifeGraph
• Possible ways to measure half-life (with problems):
  1. Number of nuclides
     • However the decayed nuclides are now nuclides of a different isotope
  2. Mass
     • However actual mass of entire sample will not change significantly since little actual mass is lost, most is converted into mass of other isotopes
  3. Activity measured - disintegrations per second (dps) or becquerel (Bq)
     • The Geiger counter can’t discriminate between 2 or more decays occurring simultaneously
     • The Geiger counter will count decay from radioactive daughter nuclide and it
• Finding the number of radionuclides present:
  • N = Number of radionuclides remaining at present time
    • N = N$_0 * \frac{1}{2}^n$ [on data sheet]
    • N$_0$ = Original # of radionuclides (at t$_0$)
    • n = Number of half-lives which have elapsed
      • n = $\frac{t}{t_\frac{1}{2}}$ [not on data sheet]
        • Where $t$ = elapsed time and $t\frac{1}{2}$ = half life of isotope

• Strong nuclear force is the force between protons and neutrons that hold the nucleus together
• Protons are like-charged particles, meaning they repel each other through electrostatic forces
  • However, strong nuclear force is much stronger, overpowering the electrostatic forces and holding the nucleus together
• Neutrons are attracted to neutrons and protons
  • There needs to be a certain number of neutrons to hold the nucleus together
    • The number of neutrons and protons need to balance out each other, too many or few neutrons can lead to the nucleus falling apart and undergoing radioactive decay
    • For larger nuclei, there needs to be more neutrons than protons to overcome the strong electrostatic force of attraction