Interactions with Matter Notes

Interactions with Matter

Electromagnetic Radiation Review

• Electromagnetic radiation is light that moves at the speed of light, denoted as $c = 3 \times 10^8 m/s$.

• It is defined by either its frequency ($f$) or wavelength ($\lambda$).

• Frequency and wavelength are related by the equation: $f = \frac{c}{\lambda}$ or $\lambda = \frac{c}{f}$.

• The energy ($E$) of electromagnetic radiation depends on its frequency or wavelength: $E = hf = \frac{hc}{\lambda}$, where $h$ is Planck's constant.

• A shortcut to calculate energy in keV if the wavelength is in nm is: $E = \frac{1.24}{\lambda}$.

Electron Capture Review

• Particle radiation is produced by unstable nuclei.

• Nuclei can be unstable if:

  • They are too heavy.

  • They have an unfavorable neutron-to-proton (N:P) ratio.

  • They are in a high-energy state instead of the ground state.

• 
  

  
  

• Too many neutrons: \beta^{-}$ decay

• Too few neutrons: \beta^{+}$decay or electron capture</p></li><li><p>Too energetic: Gamma decay or internal conversion</p></li></ul><ul><li><p>Decay types:</p><ul><li><p>$\beta^{+}$decay: Positron emission</p></li><li><p>$\beta^{-}$ decay: Electron emission

• $\alpha$ decay: Helium nuclei emission

Decay Schemes

• Example: Fluorine-18 ($^{18}F$) decays with 97% by $\beta^{+}$ and 3% by electron capture (EC).

• Maximum energy of the beta particle: $E_{\beta max} = 0.633$ MeV.

• Q-value (transitional/decay energy): $Q = 1.655$ MeV.

• Alpha and beta decay transmute elements.

• Excess energy exists due to the difference in binding energy between initial and final states, which determines the kinetic energy of decay products (including neutrinos) or gamma emission.

• $\beta^{+} decay is not possible for energies less than 1.022 MeV.

• Several decay pathways may be possible, but all excess energy is used up by the end.

Half-life ($t_{1/2}$)

• Physical half-life is determined by the decay constant ($\lambda$): $t_{1/2} = \frac{0.693}{\lambda}$.

• It is the time taken for half of the substance to decay.

• Biological half-life is the time it takes for a substance to be cleared from the body (not just radioactive substances).

• Effective half-life is a combination of physical and biological half-lives: $\frac{1}{t<em>{1/2}(eff)} = \frac{1}{t</em>{1/2}(phys)} + \frac{1}{t_{1/2}(bio)}$.

• The amount of substance remaining after time $t$: $N<em>t = N</em>0 e^{-\lambda t}$.

• Activity remaining after time $t$: $R<em>t = R</em>0 e^{-\lambda t}$.

Parent-Daughter Decay

• Examples:

  • $^{99}Mo \rightarrow ^{99m}Tc$: Parent half-life = 66 hrs, daughter half-life = 6 hrs.

  • $^{131m}Te \rightarrow ^{131}I$: Parent half-life = 30 hrs, daughter half-life = 8 days.

  • $^{226}Ra \rightarrow ^{222}Rn$: Parent half-life = 1620 yrs, daughter half-life = 4.8 days.

• Daughter products may contribute to the total overall dose.

• The concentration/activity of the daughter product is determined by relative half-lives as it decays and is produced simultaneously.

• Equilibrium types:

  • Secular Equilibrium: TD << TP, where $T<em>D$ is the daughter's half-life and $T</em>P$ is the parent's half-life.

  • Transient Equilibrium: $T<em>P \approx 10T</em>D$.

  • No Equilibrium: $T<em>P \approx \frac{1}{10}T</em>D$.

Decay Series and Radionuclides in Radiotherapy

• Decay series example: Uranium-238 ($^{238}_{92}U$).

• Table 1.2 lists characteristics of some radionuclides used in radiotherapy as either unsealed or sealed sources.

• Examples of unsealed sources include:

  • Carbon-11 ($^{11}C$), Nitrogen-13 ($^{13}N$), Oxygen-15 ($^{15}O$), Fluorine-18 ($^{18}F$) for PET imaging.

  • Phosphorus-32 ($^{32}P$) for polycythemia vera.

  • Strontium-89 ($^{89}Sr$) for bone metastases (palliation).

  • Technetium-99m ($^{99m}Tc$) for gamma camera imaging.

  • Yttrium-90 ($^{90}Y$) for radiosynovectomy.

  • Iodine-131 ($^{131}I$) for thyrotoxicosis and thyroid cancer.

  • Radium-223 ($^{223}Ra$) for prostate cancer.

• Examples of sealed sources include:

  • Cobalt-60 ($^{60}Co$) for external beam units and gamma knife.

  • Palladium-103 ($^{103}Pd$) and Iodine-125 ($^{125}I$) for brachytherapy seeds.

  • Cesium-137 ($^{137}Cs$) for brachytherapy pellets.

  • Iridium-192 ($^{192}Ir$) for brachytherapy wire.

Interactions with Matter

• In MRS (Medical Radiation Science), understanding how radiation interacts with matter is crucial for:

  • Body tissues

  • Diagnostic equipment (filters, grids, etc.)

  • Safety equipment (PPE, shielding, etc.)

  • Imaging and Treatment Machines (X-rays, PET, LINAC, etc.)

• Two important particle interactions: Electrons and Photons

Interaction of Electrons with Matter

• Once liberated from an atom (or produced as a \beta^{-}$ ray, EBRT, etc.), electrons (e^{-}$)

  • Undergo multiple scattering.

  • Experience