Updated 7 November 2023

Knowledge of the inverse-square-law applied to ionizing radiation is critical to understanding the dangers that thousands of Nuclear Weapons Technicians were unknowingly subjected to in our daily nuclear weapons tasks during the Cold War period.

While many government sponsored or conducted workshops, studies, and research regarding ionizing radiation were based on measurements from one-meter; Nuclear Weapons Technicians were frequently in close contact and actual physical contact (for hours at a time) with the exterior surfaces of the live nuclear weapons. We leaned on, directly handled, and had our hands, arms, faces, and heads in interior compartments of weapons that we disassembled for maintenance. Those tasks are described throughout this site and additional The Sound of Silence Project documentation.

Nuclear Weapons Technicians worked on live nuclear weapons, most without knowledge and training regarding the actual dangers of ionizing radiation, particularly neutron radiation, emitted from live nuclear weapons. Neutron radiation that permeated nuclear weapon exterior cases and also passed through lead shielding.

### Inverse Square Law - The intensity of energy is inversely proportional to the square of the distance

Inverse Square Law, relative to radiation, as described by the Department of Defense: *“The law which states that when radiation (thermal or nuclear) from a point source is emitted uniformly in all directions, the amount received per unit area at any given distance from the source, assuming no absorption, is inversely proportional to the square of that distance”.* ^{1}

Consider a radiation level of 1 RU (reference unit) 1 meter from the exterior surface of a weapon. Doubling the distance, moving from 1 meter to 2 meters, the amount of energy received per unit area will be 1/4th that at the 1-meter distance, or 0.25 RU. Doubling the distance from the exterior surface again, to 4 meters, the energy received will be 1/16th the original amount (0.0625 RU), and so on. The relative amount of emitted radiation per unit area drops significantly after just a few meters.

#### Inverse Square Law: Radiation increases as distance is decreased

Conversely, reducing the distance from the source by half, moving from 1 meter to 0.5 meters from the source, radiation received will be 4 times greater per unit area (4 RU). Reducing the distance to the radiation source by half again, to 0.25 meters, the energy is 16 times that at the original 1-meter distance. Continuing closer and reducing the distance by half four more times, to 0.02 meters** ^{ 2}** (2 cm), the inverse square rule indicates an increase in radiation by 4,096 times (4,096 RU); and so on, based on the inverse square law as described, assuming no absorption as DOE-DTRA Technical Procedure 4-1 states.

Note: Some numbers have been rounded to two decimal places for spacing and legibility considerations on the chart.

#### Results using four different sources, with radiation doses at 3 cm, 1 cm, and at the surface

##### Data source: Nuclear Regulatory Commission

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Footnotes:

[1] DOE-DTRA TP 4-1/TM 39-4-1/SWOP 4-1/T.O. 11N-4-1, Glossary of Nuclear Weapons Material and Related Terms, 30 July 2016, IC 1-1 10 October 2018 https://www.va.gov/vetapp20/Files7/20048516.txt

[2] Rounded up from 0.0156 meters

[3] Nuclear Regulatory Commission, NRC Instruction H-117, Chapter 5 External Dose Calculations. https://www.nrc.gov/docs/ML1121/ML11210B521.pdf Reviewed 7-23-23

[4] Sealed source: “Radioactive material that is permanently bonded or fixed in a capsule or matrix designed to prevent release and dispersal of the radioactive material.” https://ehs.unl.edu/sop/s-sealed_sources.pdf