## Ionising Radiation Quantities & Units

### Summary

The general concepts of quantities and units are introduced. The advantages of the International System of Units (SI) are mentioned, and reference made to the realisation of units for selected quantities at Standards Laboratories. Quantities and units for the measurement of ionising radiation are then discussed in detail, with particular reference to those developed for general use. References are made to the quantities defined for use in the measurement of radioactivity, dosimetry and protection.

### Contents

### 1. Fundamentals: Quantities and Units

It is important to distinguish a quantity from a unit. In everyday language the word quantity means amount, but in the field of measurement it means to characterise a physical phenomenon in terms that are suitable for numerical expression.

A physical quantity is a phenomenon capable of expression as the product of a number and a unit.

A unit is a selected reference sample of a quantity.

The Conference General des Poids et Measures (CGPM) set up by the Convention of the meter is responsible for the International System of units (SI). The International Commission on Radiation Units and Measurements (ICRU) recommends radiation units to CGPM. The International Commission on Radiological Protection (ICRP) recommends protection level quantities.

There are seven base units: the kilogram (kg), metre (m), second (s), ampere (A), Kelvin (K), mole (mol) and candela (cd).

Combining the base units forms derived units. Derived units may have special names. However some of the special names are restricted to certain quantities, e.g. Hz (s^{-1}) is the unit for frequency, but Becquerel (s^{-1}) is the unit of activity.

Quantity |
Unit |
Type of unit |
Symbol |

Length | metre | SI base unit | m |

Area | square metre | SI derived unit | m^{2} |

Energy | joule | SI derived unit with special name | J (= kg m^{2} s^{-2}) |

Absorbed dose | gray | SI derived unit with special name (restricted use) | Gy (= m^{2} s^{-2}) |

Absorbed dose | rad | Non-SI unit | rad (= 0.01 Gy) |

Note: sievert is a unit and not a quantity.

In SI units all derived units can be obtained from the base units without extra numerical factors.

### 2. Radioactivity

#### Activity, A

*A = dN/dt*

Where *dN* is the number of nuclear transformations or decay (expectation value of the number of transitions between energy states) in the time interval, *dt*.

Mathematically *dN* is understood to be the differential of an expectation value of the particle number *N*. The arguments of differential quotients are always non-stochastic quantities.

Unit: s^{-1}

Special name for the unit of activity is the becquerel (Bq).

The primary standard of activity is the 4π beta-gamma-coincidence counter. For more information consult the references.

#### Decay constant, λ

*λ = dP/dt*

Where *dP* is the probability that a nucleus decays in the time interval *dt*.

Unit s^{-1}

#### Related quantity

Half-life, *τ _{1/2}*

*τ _{1/2} = (ln 2)/λ*

The half-life is the mean time taken for radionuclides to decay to one half of their initial number.

Unit s

### 3. Radiation Field

#### Fluence, Φ

*Φ = dN/da*

Where *dN* is the number of particles incident on a sphere of cross-sectional area *da*. The use of a sphere expresses the fact one considers the area perpendicular to the direction of each particle.

Unit: m^{-2}

#### Energy fluence, Ψ

*Ψ = dR/da*

Where *dR* is the radiant energy incident on a sphere of cross-sectional area *da*.

Unit: J m^{-2}

Note: Energy is often expressed in unit of electron volts (symbol eV). It is equal to the energy gained by an electron in passing through a potential difference of 1 volt.

(eV is not an SI unit, but is accepted for use with the SI. 1 eV equals 1.6 × 10^{-19} joule approximately).

#### Fluence differential in energy, Φ(E)

The fluence differential in energy *Φ(E)*, or the distribution of fluence with respect to energy,

*Φ(E) = dΦ/dE*

Where *dΦ* is the fluence of particles with energy between *E* and *E + dE*.

Unit: m^{-2} J^{-1}

A complete description of a radiation field requires the fluence distribution as a function of: 1 particle type e.g. electrons, photons, neutrons (including any relevant quantum state, e.g. spin) 2 spatial position, 3 direction, 4 energy and 5 time.

The rate quantities, e.g. fluence rate, tend to have their own symbols. Described so far are only scalar quantities it is possible to define and use vector quantities, e.g. Vectorial fluence * Φ*.

### 4. Dosimetry

#### Kerma, K (from the acronym Kinetic Energy Released per unit Mass)

Defined as:

*K = dE _{tr}/dm*

Where *dE _{tr}* is the sum of the initial kinetic energies of all the charged particles liberated by uncharged particles in a mass

*dm*. The medium should always be specified. There are various primary standards to realise K for various particle types and energies. For a review of them consult the references.

Unit: J kg^{-1}

The special name for the unit of kerma is gray (Gy)

#### Relation to fluence

The kerma is usually expressed in terms of the distribution *Φ(E)* of the uncharged particle fluence with respect to energy. The kerma *K* is then given by

*K = ∫Φ(E) E (μ _{tr}/ρ) dE*

Where *(μ _{tr}/ρ)* is the tabulated mass energy transfer coefficient of the material for uncharged particles of energy

*E*.

#### Absorbed dose, D

*D = dε/dm*

Where *dε* is the mean energy imparted to matter of mass *dm*. Energy imparted is the energy incident minus the energy leaving the mass and minus the energy released in nuclear transformations (to stop the dose becoming negative when the mass contains a radioactive source). The medium should always be specified.

Unit: J kg^{-1}

Special name for the unit of absorbed dose is gray (Gy).

There are various primary standards to realise the Gy for various particle types and energies. For a review of calorimeters consult the references.

As the mass of a sample decreases in general the energy per unit mass will become more random (stochastic). The energy imparted per unit mass can still be defined in region *z*, but the definition of absorbed dose implies an averaging to give *D* (a non-stochastic quantity).

#### Relation to fluence

For a differential fluence *Φ(E)* of identical charged particles the absorbed dose *D* is given by:

*D = ∫Φ(E) (S/ρ) dE*

Where *(S/ρ)* is the tabulated mass stopping power of the material.

#### Under charged particle equilibrium

*D = K _{air} (μ_{tr}/ρ)_{m} / (μ_{tr}/ρ)_{air}*

### 5. Protection

#### Equivalent dose, HT

*H _{T} = ∑w_{R} D_{T,R}*

Where *D _{T,R}* is the absorbed dose (averaged over a tissue or organ

*T*) due to radiations of type

*R*and

*w*is the radiation weighting factor.

_{R}*D*can not be measured experimentally. The weighting factor is introduced to weight the absorbed dose for biological effectiveness of the particles.

_{T,R}Type and energy of radiation, R |
Radiation weighting factor, w_{R} |

Photons, all energies | 1 |

Electrons and muons, all energies | 1 |

Neutrons: | |

<10 keV | 5 |

10 to 100 keV | 10 |

> 0.1 to 2 MeV | 20 |

> 2 to 20 MeV | 10 |

> 20 MeV | 5 |

Protons, other than recoil protons, > 2 MeV | 5 |

Alpha particles, fission fragments, heavy nuclei | 20 |

Unit: J kg^{-1}

Special name for the unit of equivalent dose is sievert (Sv).

#### Effective dose, E

*E = ∑w _{T}H_{T} = ∑w_{T} ∑w_{R }D_{T,R}*

Where *D _{T,R}* is as above and

*w*is a tissue weighting factor which reflects the total detriment to health.

_{T}Tissue or organ |
Tissue weighting factor, w_{T} |

Gonads | 0.20 |

Bone marrow (red) | 0.12 |

Colon | 0.12 |

Lung | 0.12 |

Stomach | 0.12 |

Bladder | 0.05 |

Breast | 0.05 |

Liver | 0.05 |

Oesophagus | 0.05 |

Thyroid | 0.05 |

Skin | 0.01 |

Bone surface | 0.01 |

Remainder | 0.05 |

Whole body total | 1.00 |

Unit: J kg^{-1}

Special name for the unit of effective dose equivalent is sievert (Sv).

#### Protection: Operational quantities

For measurement purposes the operational quantities: ambient dose equivalent, directional dose equivalent and personal dose equivalent, are defined. Where doses are estimated from area monitoring results, the relevant operational quantities are ambient dose equivalent and directional dose equivalent.

#### Ambient dose equivalent, H*(d)

The ambient dose equivalent *H*(d)*, at a point, is the dose equivalent that would be produced by the corresponding expanded and aligned field, in the ICRU sphere at a depth *d* in millimetres on the radius opposing the direction of the aligned field. For measurement of strongly penetrating radiations the reference depth used is 10 mm and the quantity denoted *H*(10)*.

Unit: J kg^{-1}

Special name for the unit of ambient dose equivalent is sievert (Sv).

#### Directional dose equivalent, H’(d, Ω)

The directional dose equivalent *H’(d, Ω)*, at a point, is the dose equivalent that would be produced by the corresponding expanded field in the ICRU sphere at a depth *d* on a radius in a specified direction Ω. Directional dose equivalent is of particular use in the assessment of dose to the skin or eye lens.

Unit: J kg^{-1}

Special name for the unit of directional dose equivalent is sievert (Sv).

#### Personal dose equivalent, Hp(d)

The personal dose equivalent *H _{p}(d)*, is the dose equivalent in soft tissue, at an appropriate depth,

*d*, below a specified point on the body.

*H*measured with a detector which is worn at the surface of the body and covered with an appropriate thickness of tissue-equivalent material.

_{p}(d)Unit: J kg^{-1}

Special name for the unit of personal dose equivalent is sievert (Sv).

### References

- Fundamentals of Radiation Dosimetry J R Greening, medical Physics handbook, No 15 2nd Edition 1985 Adam Hilger, Bristol
- ICRU Report 60 Fundamental Quantities and Units for Ionising Radiation 1998 http://www.icru.org/
- ICRP Report 60 1990 Recommendations of the International Commission on Radiological Protection http://www.icrp.org/
- Bureau International des Poids et Mesures (BIPM) http://www.bipm.fr/
- National Physical Laboratory (NPL)
- National Institute of Standards and Technology (NIST) http://physics.nist.gov/cuu/index.html
- National Radiological Protection Board (NRPB) http://www.nrpb.org.uk/
- Campion, P.J., 1959. The standardization of radioisotopes by the beta-gamma coincidence method using high efficiency detectors.
*Int. J. Appl. Radiat. Isot.*(4) 232-248. - ICRU Report 52 1994 Particle Counting in Radioactivity Measurement
- NPL Calorimetry: The evolution so far
- A R S Marsh, T T Williams. 50 kV Primary Standard of Exposure 1978 Design of Free-Air Chamber;
*NPL Report***RS(EXT) 54**; April 1982 - BIR Working Party on SI Units. 1981 Conversion to SI units in radiology. British
*Journal of Radiology*, (54) 377-380. - ICRU Report 51 Quantities and Units in Radiation Protection 1993 http://www.icru.org/
- Ionising Radiation Regulations and supporting Approved Code of Practice 1999

**Last Updated: 1 Aug 2012**

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