The Mathematics of Radiation Protection

These articles and guidance look at the mathematics (maths) associated with radiation protection / health physics including half-life, inverse square law, statistics, instrumentation, famous physics equations and much more. If you like your radiation safety served with maths, then this resource section is for you!

  • Radioactive source holders - Dose rate through an aperture

    Published: Apr 23, 2024

    Source: Dr Chris Robbins, Grallator / Ionactive radiation protection resource

      Tags:
    • Shielding aperture
    • Nuclear gauge
    • Nuclear density gauge
    • Radiation through an aperture
    • Whole body exposure
    • effective dose
    • Nuclear gauge accident dose rates
    • Collimated radiation
    • Inverse square law
    • Multi-phase flow meter
    • Radioactivity

    This article, and our discussions with Dr Chris Robbins of Grallator, was born from a consideration of when a radioactive source holder (such as that fitted as part of a nuclear gauge) might become detached during a radiation accident, such that the radiation from the source is exposed directly through a small aperture. This is reasonably foreseeable compared to a radioactive source which might be completely exposed (unshielded). What would the dose rates be at a certain distance from the source holder, and what % of the trunk of the body would be exposed? This article considers the maths / physics behind this situation which has been developed for Ionactive by Chris. Ionactive has then taken the results of this analysis and shown how it would apply to a real world radiation accident. 

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  • Calculate an estimate of x-ray dose rate from an x-ray tube given kV and mA

    Published: Mar 24, 2024

    Source: Dr Chris Robbins, Grallator/ Ionactive Radiation Protection Resource

      Tags:
    • X-ray
    • X-ray dose rate
    • X-ray generator
    • mA
    • kV
    • Calculate x-ray tube output
    • Formula for x-ray tube output
    • Calculate x-ray tube dose rate
    • Anode
    • Cathode
    • Bremsstrahlung x-rays
    • Characteristic X-rays
    • Tungsten target
    • Inverse square law
    • Energy Absorption
    • Mass Energy Absorption Coefficient
    • Gray (Gy)
    • NDT X-ray tube
    • Medical X-ray tube
    • Radiation Protection Adviser (RPA)

    How do you calculate an estimate of dose rate from an X-ray tube give kV and mA? In this resource we consider a 'ballpark' estimate of radiation dose rate using some physics principles, including an estimate of % bremsstrahlung from an anode target, combined with a calculation of power density and consideration of average energy absorption rate.

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  • When \( 1/d^2 \) breaks down - part 2: area source

    Published: Mar 22, 2024

    Source: Dr Chris Robbins, Grallator

      Tags:
    • 1/d2 for an area source
    • Inverse square law
    • radiation
    • radioactive area source
    • Radiation protection mathematics
    • Maths for radiation safety

    When \( 1/d^2 \) breaks down - part 2: area source. Using some mathematics to explore how the inverse square law works with a radiation area source.

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  • When \(1/d^2\) breaks down - part 1: line source

    Published: Mar 22, 2024

    Source: Dr Chris Robbins, Grallator

      Tags:
    • 1/d2 for a line source
    • Inverse square law
    • radiation
    • radioactive line source
    • Radiation protection mathematics
    • Maths for radiation safety

    When \( 1/d^2 \) breaks down - part 1: line source. Using some mathematics to explore how the inverse square law works with a radiation line source.

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  • The accumulated radiation dose when moving up to a source

    Published: Nov 27, 2023

    Source: Dr Chris Robbins, Grallator

      Tags:
    • Dr Chris Robbins
    • Grallator
    • Accumulated dose
    • Maths in radiation protection
    • Radioactive source
    • accumulated radiation exposure moving towards a source
    • Inverse square law
    • Point source

    Consider the situation where you move up to a radioactive source, perform some operations for a period of time, and then move away. What total dose will be received?

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  • Physical, biological and effective half-life

    Published: Sep 29, 2021

    Source: Dr Chris Robbins, Grallator

      Tags:
    • Physical half-half
    • Biological Half-Life
    • Effective Half-Life
    • Half-Life
    • Radiation Protection
    • Health Physics
    • Maths
    • Mathematics
    • Radioactive Decay
    • Radioactivity
    • Radiation physics

    This technical mathematics article is written by Dr Chris Robbins of Grallator Limited. This article looks at Physical, biological and effective half-life and the mathematics behind them.

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