# 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
• Whole body exposure
• effective dose
• Nuclear gauge accident dose rates
• Inverse square law
• Multi-phase flow meter

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.

• ## 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

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.

• ## 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

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.

• ## 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

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.

• ## 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
• 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?

• ## 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
• Health Physics
• Maths
• Mathematics