Every radioactive source is on a clock. From the moment it leaves the reactor or accelerator, its activity decreases according to a fixed mathematical law that depends only on the isotope's half-life. Understanding this decay process is essential for three practical reasons: calculating current source activity for dose rate and boundary determinations, planning source replacements before output drops below useful levels, and managing source disposal when the activity is low enough for waste classification or decay-in-storage programs.
This guide covers the decay equation, half-life data for the isotopes most common in industrial and gauging applications, how to build decay tables and replacement schedules, the regulatory requirements for source tracking, and the options for end-of-life source management.
The Decay Equation
Radioactive decay is a first-order process: the number of atoms that decay per unit time is proportional to the number of atoms present. This gives an exponential decrease in activity over time:
A(t) = A&sub0; × (1/2)^(t / t½)
Where A(t) is the activity at time t, A&sub0; is the initial activity at the reference (calibration) date, t is the elapsed time, and t½ is the half-life. The equation can also be written using the decay constant λ: A(t) = A&sub0; × e^(-λt), where λ = ln(2) / t½ = 0.693 / t½.
Both forms are mathematically equivalent. The half-life form is more intuitive for quick estimates: after one half-life, half remains; after two half-lives, one quarter remains; after ten half-lives, about one thousandth remains. The exponential form is more convenient for calculating decay constants and for working with computer programs.
An important property: the decay rate is independent of temperature, pressure, chemical state, and all other external conditions. A Cs-137 source decays at the same rate whether it is in a laboratory, buried underground, or orbiting in space. This is why the half-life is a true physical constant for each isotope, not an approximation.
A(t) = A&sub0; × (1/2)^(t / t½)
Equivalent form: A(t) = A&sub0; × e^(-0.693 × t / t½)
After n half-lives, the remaining fraction is (1/2)^n. After 10 half-lives, about 0.1% of the original activity remains.
Radioactive Decay Calculator
Calculate current source activity from original calibrated activity and elapsed time using the decay equation. Find when a source reaches a target activity for replacement or disposal planning.
Half-Life Data for Common Industrial Isotopes
The following half-life values are from the NNDC (National Nuclear Data Center, Brookhaven National Laboratory) evaluated nuclear data. These are the accepted reference values for regulatory and practical calculations.
- Ir-192: 73.83 days. Used in industrial radiography. Sources are replaced every 3 to 4 months as activity drops below useful levels.
- Co-60: 5.271 years. Used in industrial radiography (less common than Ir-192 in the U.S.), irradiators, and some gauging applications. Sources are replaced every 5 to 7 years depending on the application.
- Cs-137: 30.17 years. Used in level gauges, density gauges, well-logging sources, and fixed industrial gauges. Effectively permanent for most facility planning purposes. A source purchased today will still have 50% of its original activity in 2056.
- Am-241: 432.2 years. Used in smoke detectors, moisture-density gauges (neutron source for moisture measurement), and portable XRF analyzers. Effectively constant activity for any human planning horizon.
- Se-75: 119.78 days. Used in industrial radiography as a lower-energy alternative to Ir-192, particularly for thin-wall piping. Replaced every 6 to 8 months.
- Kr-85: 10.76 years. Used in some thickness gauges and gas chromatography detectors.
- H-3 (tritium): 12.32 years. Used in self-luminous signs and some gas chromatography detectors.
Half-life ranges for industrial isotopes span six orders of magnitude: from 73.83 days (Ir-192) to 432 years (Am-241). Short-lived sources require frequent replacement scheduling. Long-lived sources require long-term storage and disposal planning.
Source Replacement Scheduling
Sources used in radiography and gauging applications must be replaced when the activity drops below the level required for the application. For radiography, this is typically when exposure times become impractically long. For gauging, it is when the count rate drops below the instrument's statistical precision threshold.
Ir-192 radiography sources are typically replaced every 3 to 4 half-lives (about 220 to 295 days). At 3 half-lives, the activity is 12.5% of the original. A source loaded at 100 Ci will be at 12.5 Ci after 221 days. Exposure times increase by a factor of 8 compared to the fresh source, which makes field radiography impractical for thick-wall specimens. Most radiography companies establish a minimum usable activity based on their typical shot configurations and replace before reaching it.
Cs-137 level and density gauges rarely need source replacement due to decay. The 30-year half-life means a gauge loses only 2.3% of its activity per year. Over a typical 20-year gauge service life, the source retains about 63% of its original activity. Gauge replacement is more often driven by electronic obsolescence or mechanical wear than by source decay.
To calculate when a source will reach a target replacement activity: t = t½ × log&sub2;(A&sub0; / A(target)). For an Ir-192 source starting at 100 Ci with a minimum usable activity of 15 Ci: t = 73.83 × log&sub2;(100/15) = 73.83 × 2.74 = 202 days. Order the replacement source about 2 to 3 weeks before this date to allow for delivery and scheduling.
Set a calendar reminder at 70% of the expected source life to initiate the replacement source order. For Ir-192, this is about 150 days after loading a new source. This provides adequate lead time for procurement, shipping, and scheduling the source exchange.
Radioactive Decay Calculator
Calculate current source activity from original calibrated activity and elapsed time using the decay equation. Find when a source reaches a target activity for replacement or disposal planning.
Decay-in-Storage Programs
Short-lived radioactive materials can be held until they decay to background levels, then disposed of as non-radioactive waste. This is called decay-in-storage (DIS). NRC guidance (and most Agreement State regulations) allows DIS for materials with half-lives of 120 days or less, provided the material is held for at least 10 half-lives and is surveyed before disposal to confirm the activity is indistinguishable from background.
After 10 half-lives, the activity is reduced to about 0.1% (1/1024) of the original. For practical purposes, this is below the detection limit for most sources in their stored configuration.
Ir-192 (73.83 days) is the most common industrial isotope eligible for DIS. After 10 half-lives (738 days, about 2 years), a source that started at 100 Ci is at approximately 0.1 Ci. After holding until the activity is indistinguishable from background (survey with a sensitive detector on contact with the source capsule), the capsule can be disposed as non-radioactive metal waste.
Se-75 (119.78 days) also qualifies. Ten half-lives is about 1,198 days (3.3 years). Because the half-life is just under the 120-day cutoff, it is eligible under most DIS programs.
Materials with half-lives over 120 days (Co-60, Cs-137, Am-241) do not qualify for DIS. These sources must be returned to the manufacturer, transferred to another licensee, or disposed through a licensed radioactive waste broker. Source manufacturers like Eckert & Ziegler, QSA Global, and others typically offer source return programs for end-of-life sealed sources.
Before disposing of any decay-in-storage material as non-radioactive waste, survey every item with a sensitive detector (pancake GM or NaI probe) to confirm the reading is indistinguishable from background. Document the survey with instrument model, serial number, calibration date, background reading, and item reading. Retain this record.
Regulatory Requirements for Source Tracking
The NRC requires licensees to maintain records of all sealed sources from receipt through disposal. Key regulatory requirements include:
10 CFR 20.2001 (Disposal): Radioactive material may only be disposed by transfer to an authorized recipient, by decay-in-storage where permitted, or by other methods specifically authorized in the license. Unauthorized disposal is a violation with significant penalties.
10 CFR 30.35 (Financial assurance): Licensees possessing sealed sources above certain activity thresholds must maintain financial assurance (decommissioning funding) to ensure sources can be properly disposed when the license is terminated.
10 CFR 34.27 (Leak testing): Sealed sources used in radiography must be leak tested at intervals not to exceed 6 months. Each source must be individually tested and the results recorded.
10 CFR 34.29 (Inventory): Radiography licensees must conduct a quarterly physical inventory of all sealed sources and devices. The inventory must include the model, serial number, and activity (calculated from the most recent calibration certificate using the decay equation) of each source.
National Source Tracking System (NSTS): Sources in Category 1 and Category 2 (as defined in 10 CFR 20.2207) must be reported to the NRC's NSTS within specified timeframes upon receipt, transfer, or disposal. Most industrial radiography sources above about 0.8 Ci Ir-192 or Co-60 fall into these categories. The NSTS was established to enhance accountability for high-risk sources.
Quarterly source inventories under 10 CFR 34.29 require calculating current activity from the calibration certificate using the decay equation. This is not optional. The inventory must reflect the activity on the date of the inventory, not the original calibration activity.
End-of-Life Source Management Options
When a sealed source is no longer needed, the licensee has several options depending on the isotope, activity, and source condition:
Return to manufacturer: Most major source manufacturers accept returned sources under their source return programs. This is the simplest option and transfers all disposal responsibility to the manufacturer. There is usually a fee, which may be substantial for high-activity or damaged sources. Some purchase agreements include a return provision in the original price.
Transfer to another licensee: If another company can use the source, it can be transferred under a properly documented transfer. The receiving licensee must be authorized to possess the isotope and activity being transferred. Both parties must maintain transfer records.
Decay-in-storage: For isotopes with half-lives of 120 days or less (Ir-192, Se-75), hold the source for at least 10 half-lives, survey to confirm it is at background, and dispose as non-radioactive waste. Document everything.
Licensed waste broker: Companies like EnergySolutions, Waste Control Specialists, and others accept sealed sources for disposal at licensed radioactive waste disposal facilities. The broker handles packaging, transport, and disposal documentation. Costs vary by isotope, activity, and source form.
Orphan source: If a licensee cannot afford to dispose of sources and the license is being terminated, the NRC or Agreement State may need to arrange disposal using the financial assurance funds. If no financial assurance exists, the source may become an "orphan" source, which is a significant regulatory and safety concern. This situation should be avoided through proper planning and financial assurance from the start of the license.
Build source disposal costs into the procurement budget. When ordering a new source, get a quote for the return/disposal at the same time. Knowing the end-of-life cost up front prevents unpleasant financial surprises when the source needs to be replaced or the license is terminated.
Radioactive Decay Calculator
Calculate current source activity from original calibrated activity and elapsed time using the decay equation. Find when a source reaches a target activity for replacement or disposal planning.