00 Foundations
Photoelectric scaling
τ/ρ scales roughly as Zⁿ / Eᵐ between absorption edges.
Listen
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Simulation
Photoelectric scaling — Change the numbers; the scene follows.
Where it works
Radiography room
Patient
At the patient entrance — skin dose, subject contrast, photoelectric absorption in tissue.
Open this machineFormula
Variables
Results
ratio
τ/ρ ratio
544.6798
Explanation
What it means
The photoelectric mass attenuation coefficient rises steeply with atomic number and falls with photon energy, except at absorption edges. A working rule is n ≈ 3–4 and m ≈ 3–3.5. That is why iodine (Z=53) and barium (Z=56) are x-ray contrast agents, and why bone (effective Z ~ 13) absorbs more than soft tissue (Z ~ 7.4) at diagnostic energies. This is a working relation in Radiation physics.
Where it is used
Clinically it sits on the Radiography room — Patient. At the patient entrance — skin dose, subject contrast, photoelectric absorption in tissue. Radiation physics lives at the x-ray target, the linac head, and inside the patient: how a photon is born, how it scatters, and how it dies. Use these relations before you trust a spectrum, a wall, or a kV-versus-MV contrast argument.
Radiography room · Open this machineHow to use it
Compare two materials or two energies. Default n=3.2, m=3.2. Example: raising Z from 7.4 (tissue) to 53 (iodine) at the same energy multiplies τ/ρ by (53/7.4)^3.2 ≈ 500. Change one input and watch the curve and the simulation follow.
Symbols
- Z₁Atomic number 17.4
- E₁Energy 130 keV
- Z₂Atomic number 253
- E₂Energy 230 keV
- nZ exponent3.2
- mE exponent3.2
Worked example
A typical case from the default values: Z₁ = 7.4 (Atomic number 1); E₁ = 30 keV (Energy 1); Z₂ = 53 (Atomic number 2); E₂ = 30 keV (Energy 2); n = 3.2 (Z exponent); m = 3.2 (E exponent). Substituting into the relation gives ratio = 544.6798. These are teaching numbers — align them with your machine.
Typical values give
- ratio = 544.6798
Where it comes from
The displayed formula is the working relation. τ/ρ scales roughly as Zⁿ / Eᵐ between absorption edges. Usual reference: Bushberg / Attix. Derive it in the specialty lesson, then return here to pin the numbers.
Reference: Bushberg / Attix
Assumptions & limits
Valid only between K/L edges and as a ratio estimate — not an absolute cross section. Coherent and Compton components are separate. At MV energies photoelectric is usually negligible except in high-Z shielding.
Pitfalls
Do not mix free-electron Compton kinematics with photoelectric-dominated kV imaging. Check keV versus MeV, and never treat a spectrum as one photon. Valid only between K/L edges and as a ratio estimate — not an absolute cross section. Coherent and Compton components are separate. At MV energies photoelectric is usually negligible except in high-Z shielding.
Keep this
Photons do not deposit dose; the electrons they set in motion do. Valid only between K/L edges and as a ratio estimate — not an absolute cross section. Coherent and Compton components are separate. At MV energies photoelectric is usually negligible except in high-Z shielding.
In this specialty