Dr Mark Marais

May 2025

Physical Principles

of Radiation Safety & Protection

Dr Mark Marais - 2025

• understand the two categories of radiation hazards:
• external, and,
• internal
• understand controlling radiation hazards by applying the following principles:
• distance
• shielding
• time
• avoidance
• minimisation
• containment

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let’s aim to

Dr Mark Marais - 2025

Dr Mark Marais - 2025

Distance - Inverse Square Law

the brightness or intensity of the spray paint will fade the further we are from the wall if we spray the same amount each time, as the paint will be spread over a greater area

for 1 d of measure away from the wall the paint is spread over 1 square unit

for 2 d of measure away from the wall the paint is spread over 2 square units

for 3 d of measure away from the wall the paint is spread over 3 square units

1 d

2 d

3 d

Intensity

Dr Mark Marais - 2025

where,

D is the dose rate

r is the distance from source

K is constant for a particular source

Distance

As a rough estimation, the inverse square law can be applied to determine the change in external penetrating radiation exposure with change in distance from the radiation source.

The inverse square law may be written as:

Dr Mark Marais - 2025

⇒ X₁r₁² = X₂r₂²

where X is the eXposure dose

example

The exposure at 2 m from a particular γ source is 50 R.

At what distance will it give an exposure of 2 R?

X₁r₁² = X₂r₂²

⇒ (50)(2)² = (2)r₂²

⇒ r₂² = 100 m²

⇒ r₂ = 10 m

Distance

Dr Mark Marais - 2025

Usually for a gamma-ray source, its activity is stipulated in mCi (e.g. a 5 mCi source of ²²Na).

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Distance

where,

D is the dose rate

C is the radioactivity of the source

E is the total gamma ray energy in MeV

r is the distance from the source

Dr Mark Marais - 2025

If this is known, then the approximate dose rate can be calculated from the expression:

Distance

example

Calculate the approximate dose rate at a distance of

3 metres from a 180 mCi source of Cobalt-60.

This source emits two gamma-rays per disintegration

of energies 1.17 and 1.33 MeV.

Dr Mark Marais - 2025

Shielding

• If often arises that staff have to work in the close vicinity of an x-ray tube, e.g., during screening.
• In such cases, it is necessary to place a shield between the tube and the person concerned.
• The thickness of the shield is chosen such that it will attenuate the intensity of the beam to a safe level.
• Shielding is also commonly used to protect workers against radiation from radioactive sources (especially when they have to work in close vicinity of the radiation source).

Dr Mark Marais - 2025

Attenuation versus Absorption

When photons interact with matter, one of three things can happen to the photons.

It can be:

• Transmitted - the photon passes through the

material without being affected

• Scattered - The photon is deflected from its

original path

• Absorbed - The photon's energy is completely

transferred to the material, and no

photon emerges

Shielding

Dr Mark Marais - 2025

Shielding – HVL & TVL

Dr Mark Marais - 2025

The Half-Value Layer (HVL) is the amount of shielding it takes to reduce the incident radiation by half.

The Tenth-Value Layer (TVL) is the amount of shielding it takes to reduce the incident radiation by one-tenth.

Shielding – HVL & TVL

Dr Mark Marais - 2025

Both depend on the energy of the radiation and the type of shielding.

HVL, transmission through shielding, attenuation of a radiation beam, by using the plot and table

this refers to the amount of radiation which gets through the shielding or barriers

Shielding – HVL & TVL

understand

Dr Mark Marais - 2025

Shielding – HVL & TVL

Dr Mark Marais - 2025

Shielding – HVL & TVL

Dr Mark Marais - 2025

Intensity for a heterogeneous (polychromatic) beam of direct x-ray

• due to the inhomogeneity of a heterogeneous beam, successive half-value thicknesses will increase in magnitude
• calculation of the barrier thickness, as was done before, will lead to an underestimation of the protective thickness required.
• instead, we can use published attenuation curves to find barrier thickness
• (the same goes for tenth-value thicknesses)

Shielding – HVL & TVL

Dr Mark Marais - 2025

Dr Mark Marais - 2025

Shielding – HVL & TVL

Calculate the thickness of lead required to reduce the intensity of direct heterogeneous radiation, of 100 kV X-rays at some point, from 10 000 mR/week to 100 mR/week.

From the curve of 100 kV X-rays attenuated by lead, about 0.58 mm lead is required

example

Roentgen per time measures the rate of x-ray or gamma radiation exposure.

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This unit quantifies the intensity of radiation in a specific location at a given moment by indicating the amount of ionization produced in the air over a set time period.

0.58 mm

Dr Mark Marais - 2025

Where attenuation curves are available for lead, but not for other materials, the required protective thickness is determined in terms of lead by using the previous curves, and the corresponding thickness of the other material is found by using the lead equivalent of the other material.

Shielding – lead equivalent

Dr Mark Marais - 2025

Shielding – lead equivalent

The lead equivalent of a barrier material for a given beam energy is the thickness of lead that would attenuate the same amount of radiation as the given material when exposed to the same radiation.

Dr Mark Marais - 2025

The dose (or exposure) accumulated by a person working in an area having a particular exposure rate is directly proportional to the amount of time that they spend in that area.

The work should therefore be executed with as much speed as possible. It must be borne in mind that the longer the exposure, the greater the chance of radiation injury.

Time

Dr Mark Marais - 2025

Usually the dose rate is stipulated for a certain working area.

Time

Dr Mark Marais - 2025

The dose can then be calculated by using the simple relationship:

received by worker

stipulated for working area

spent in working area

Thus, if we reduce the exposure by half, the dose rate reduces by half.

Time

A certified radiation worker is permitted to receive up to 100 mrem/week.

How many hours of each week can the worker spend in an area having an average dose rate of 10 mrem?

example