00 Foundations

Moseley Kα characteristic energy

Kα x-ray energy from Moseley’s law: E ≈ 10.2 (Z−1)² eV.

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Simulation

Moseley Kα characteristic energy — Change the numbers; the scene follows.

Where it works

Radiography room

X-ray tube

At the focal spot in the tube housing — spectrum, output, SID geometry, and unsharpness start here.

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Formula

E_{K\alpha}=10.2\,(Z-1)^2\,\mathrm{eV}=13.6\,(Z-1)^2\left(1-\tfrac{1}{4}\right)\,\mathrm{eV}

Typical values

Variables

Z · Atomic number

Results

E_Kα
Kα energy
54.3558keV
≈K-edge
Approx. K-edge
63.5963keV
kVp_min
Minimum kVp to produce Kα
63.5963kV

Curve

Explanation

E_{K\alpha}=10.2\,(Z-1)^2\,\mathrm{eV}=13.6\,(Z-1)^2\left(1-\tfrac{1}{4}\right)\,\mathrm{eV}

What it means

Characteristic x-rays are emitted when an outer electron fills a K-shell vacancy. Moseley treated the K-shell as hydrogen-like with screening constant 1, so E_Kα = 13.6 (Z−1)² (1 − 1/4) eV. Tungsten (Z=74) predicts ~54 keV; the measured Kα is 59.3 keV. Molybdenum Kα is 17.5 keV — the reason Mo anodes are used in mammography. This is a working relation in Radiation physics.

Where it is used

Clinically it sits on the Radiography room — X-ray tube. At the focal spot in the tube housing — spectrum, output, SID geometry, and unsharpness start here. 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 machine

How to use it

Enter atomic number Z of the anode (or contrast agent). Read Kα in keV and the tube kVp that just produces it (must exceed the K-edge, slightly above Kα). Presets cover W, Mo, Rh, Cu, I, Ba. Change one input and watch the curve and the simulation follow.

Symbols

ZAtomic number74

Worked example

A typical case from the default values: Z = 74 (Atomic number). Substituting into the relation gives E_Kα = 54.3558 keV; ≈K-edge = 63.5963 keV; kVp_min = 63.5963 kV. These are teaching numbers — align them with your machine.

Typical values give

E_Kα = 54.3558keV
≈K-edge = 63.5963keV
kVp_min = 63.5963kV

Where it comes from

Bohr: E = 13.6 Z_eff² (1/n₁² − 1/n₂²) eV. For Kα, n₁=1, n₂=2, Z_eff = Z−1 (the remaining K electron screens one charge).

Reference: Moseley 1913 / Bushberg

Assumptions & limits

Screening constant is 1; L-lines and Kβ (≈1.1 Kα) are omitted. Real K-edges are a few keV above Kα (W K-edge 69.5 keV). Not valid for Z < ~10.

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. Screening constant is 1; L-lines and Kβ (≈1.1 Kα) are omitted. Real K-edges are a few keV above Kα (W K-edge 69.5 keV). Not valid for Z < ~10.

Keep this

Photons do not deposit dose; the electrons they set in motion do. Screening constant is 1; L-lines and Kβ (≈1.1 Kα) are omitted. Real K-edges are a few keV above Kα (W K-edge 69.5 keV). Not valid for Z < ~10.

In this specialty

Radiation physics