Formula & Calculator
Inverse Square Law for Radiation Intensity
Calculates how radiation intensity from a point source decreases with distance, following the inverse square law.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| I2 | Intensity at new distance | |
| I1 | Intensity at reference distance | |
| d1 | Reference distance | |
| d2 | New distance |
What it means
The inverse square law states that the intensity (I) of radiation from a point source is inversely proportional to the square of the distance (d) from the source, assuming no absorption or scattering. Mathematically, I₂ = I₁ (d₁/d₂)². This relation holds for uncharged radiation like gamma rays and neutrons in a vacuum or in air with negligible attenuation. It is used to estimate dose rates at various distances, to design radiation shielding, and to establish exclusion zones around radioactive sources. In practice, the law must be modified when shielding or scattering is significant. Understanding this law is essential for radiation safety, especially for handling sealed sources and for planning industrial radiography or medical procedures. It helps reduce exposure by using distance as a primary protection measure.
Worked example
Inverse Square Law – Two Examples
Real‑World| Parameter | Value |
|---|---|
| I₁ | 100 mR/hr |
| d₁ | 1 m |
| d₂ | 2 m |
| Parameter | Value |
|---|---|
| I₁ | 50 µSv/hr |
| d₁ | 1 m |
| d₂ | 5 m |
Common mistakes
- Inverse square law: I₂ = I₁·(d₁/d₂)² – assumes a point source emitting equally in all directions.
- Intensity I: Radiation intensity (e.g., flux, dose rate) – in the same units at both points.
- Distances d₁ and d₂: Measured from the source – not the distance between the two measurement points.
- No attenuation: The law applies in a vacuum or air (no absorption/scattering).
- Extended sources: For line or area sources, the law is different (e.g., inverse distance for line sources).
Applications
The inverse square law for radiation intensity, I₂ = I₁·(d₁/d₂)², states that the intensity of radiation from a point source decreases with the square of the distance. This is fundamental for radiation shielding and for determining safe distances from sources. Health physicists use it to calculate exposure rates at various distances, to design area monitoring, and to establish controlled zones around radioactive sources. In radiotherapy, it is used to position patients relative to the source. In nuclear facilities, it guides the placement of detectors and the layout of work areas. By applying the inverse square law, professionals can effectively manage radiation exposure and ensure safety without unnecessary shielding.
- Design of controlled zones and exclusion distances
- Calculation of exposure rates for workers and public
- Radiotherapy source positioning and patient setup
- Placement of radiation monitoring instruments
- Emergency response planning for radiation incidents