04 Protection

Time, distance, and shielding

Dose from a reference rate with time, inverse square, and transmission.

Play lecture Cast to TV

Listen

Listen · English

Simulation

Time, distance, and shielding — Change the numbers; the scene follows.

Where it works

Treatment vault

Maze

Along the maze — stay time and inverse-square from the last scatter to the exit.

Open this machine

Formula

D = \dot{D}_0\cdot t\cdot\left(\frac{d_0}{d}\right)^2\cdot B

Variables

Ḋ₀ · Reference dose ratemSv/hd₀ · Reference distancemd · Distancemt · Exposure timehB · Transmission

Results

D
Dose
0.5mSv

Curve

Explanation

D = \dot{D}_0\cdot t\cdot\left(\frac{d_0}{d}\right)^2\cdot B

What it means

The three levers of external protection are time, distance and shielding: D = Ḋ₀ t (d₀/d)² B. Cut time, increase distance (inverse square), and insert a barrier of transmission B. ALARA in one line. This is a working relation in Radiation protection.

Where it is used

Clinically it sits on the Treatment vault — Maze. Along the maze — stay time and inverse-square from the last scatter to the exit. Protection equations are the wall, the occupancy factor, and the badge: time, distance, shielding, and WUT. They turn a room into a legal design.

Treatment vault · Open this machine

How to use it

Start from a measured or calculated rate at d₀. Set B = 1 for no shield. Pair with HVL/TVL calculators to turn a desired B into thickness. Change one input and watch the curve and the simulation follow.

Symbols

Ḋ₀Reference dose rate2 mSv/h
d₀Reference distance1 m
dDistance2 m
tExposure time1 h
BTransmission1

Worked example

A typical case from the default values: Ḋ₀ = 2 mSv/h (Reference dose rate); d₀ = 1 m (Reference distance); d = 2 m (Distance); t = 1 h (Exposure time); B = 1 (Transmission). Substituting into the relation gives D = 0.5 mSv. These are teaching numbers — align them with your machine.

Typical values give

D = 0.5mSv

Where it comes from

The displayed formula is the working relation. Dose from a reference rate with time, inverse square, and transmission. Usual reference: NCRP / Cember, Health Physics. Derive it in the specialty lesson, then return here to pin the numbers.

Reference: NCRP / Cember, Health Physics

Assumptions & limits

Point-source inverse square in air plus a simple transmission factor (no buildup, no scatter around the shield, no energy change). Occupancy and use factors belong in the barrier equation.

Pitfalls

Tenth-value layers are for the broad beam in that material and that energy — not a photocopy from another bunker. Occupancy T is not a guess; it is a use pattern. Inverse-square fails against a large scatter source. Point-source inverse square in air plus a simple transmission factor (no buildup, no scatter around the shield, no energy change). Occupancy and use factors belong in the barrier equation.

Keep this

Time, distance, shielding — in that order — then calculate the wall. Point-source inverse square in air plus a simple transmission factor (no buildup, no scatter around the shield, no energy change). Occupancy and use factors belong in the barrier equation.

In this specialty

Stay time Transmission from HVL and TVL Required thickness Required barrier transmission Thickness from TVL₁ and TVLₑ Equivalent dose Effective dose (single tissue)Head leakage dose Patient scatter at 1 m Quality factor (older H = QD)Weekly design limit P Workload, use and occupancy WUT Primary-barrier transmission B Thickness from HVL / TVL I-131 patient-release dose Lead equivalence Dose-limit remaining Skyshine (NCRP 151 approximation)Photoneutron TVL (concrete)

Radiation protection