Source Activity Decay Calculator
A source projector certificate shows the activity on day of calibration — never the activity on the day you load the camera. Iridium-192 drops 1% per day; on day 75 you have half the curies you started with, and on day 150 you have a quarter. This tool runs the exponential decay so the exposure-time and safe-distance numbers you generate match the source as it stands today, not as it left the supplier.
How it works
Radioactive decay is first-order: A(t) = A₀ × e^(-λt) where λ = ln(2) / half-life. Every isotope has a fixed half-life: Ir-192 = 73.83 days, Co-60 = 5.27 years (1925 d), Se-75 = 119.78 days, Cs-137 = 30.05 years. Multiply current activity by the inverse-square distance factor and you have a working dose rate at any point in the source's service life.
Formula
A(t) = A₀ × exp(-λ × t) ; λ = ln(2) / T½
A(t) = A₀ × exp(-λ × t) ; λ = ln(2) / T½Worked example
A 100 Ci Ir-192 source 75 days post-calibration. T½ = 73.83 days, λ = ln(2)/73.83 = 0.00939/day. A(75) = 100 × e^(-0.00939 × 75) = 100 × e^(-0.704) = 49.3 Ci. Plug 49.3 Ci into the safe-distance calculator instead of the certificate value — the difference between 100 Ci and 49 Ci is the difference between a 50 m and a 35 m boundary.
| Variable | Value |
|---|---|
| input: initialActivity | 100 |
| input: isotope | Ir-192 |
| input: daysElapsed | 75 |
| output: currentActivity_Ci | 49.3 |
| output: percentRemaining | 49.3 |
When to use this tool
Use every time you load a source projector, plan a shoot more than a week out, write a shielding letter, or audit a vendor's exposure calculation. Required before every Ir-192 job because the activity is meaningfully different week to week.
Limitations
Where this calculator stops being accurate:
- Assumes no source replacement or top-up. If the assembly was re-loaded mid-cycle, restart from the new calibration date.
- Cobalt-60 decay over a typical 5-year service life drops activity to 51% — significant but slower than Ir-192.
- Se-75 has a slightly more complex decay scheme; the simple A₀ × e^(-λt) is accurate to within 0.5% across normal service intervals.
- Half-life values vary by source: ANSI N43.3 lists 73.83 d for Ir-192; NIST gives 73.827 d — for field work the variation is irrelevant.
- Does not account for source self-absorption, which becomes noticeable for very large source pellets (>3 mm).
Frequently Asked Questions
How often should I recompute source activity?
For Ir-192 every shift — the source loses ~1% per day, so a one-week-old activity reading is 7% off. For Co-60 weekly is enough; the half-life is 5.27 years and weekly drift is 0.03%. Operating procedures under 10 CFR 34.43 require source activity tracking in the daily utilization log, and many DOT type-B transport documents require the activity to be updated to within 24 hours of shipment.
What half-life value is authoritative?
NIST and IAEA publish the reference values: Ir-192 = 73.827 ± 0.013 days, Co-60 = 1925.28 ± 0.14 days (5.2711 years), Se-75 = 119.779 ± 0.004 days, Cs-137 = 30.05 ± 0.08 years. ANSI N43.3 rounds these to four-significant-figure values for industry use. The differences are immaterial in the field but show up in audit calculations — pick one source and use it consistently.
Can a depleted Ir-192 source still be used?
Mechanically yes, until DOT/NRC type-B encapsulation expires (10 years for most projector sources per 10 CFR 71). Practically no — below ~10 Ci of Ir-192 the exposure times for a quarter-inch steel weld push past 30 minutes per shot, making the job uneconomical. Industry rule of thumb: replace at 25% of original activity, which is two half-lives or ~148 days for Ir-192.
How does decay affect exposure time?
Inversely. Exposure time at constant film density scales as 1/activity, so a source at 50% activity needs twice the exposure. A weld that took 4 minutes on day 0 takes 8 minutes on day 73.83 (one half-life), 16 minutes on day 147, and 32 minutes by day 220. This is exactly why the RT exposure-time tool pulls current activity from this decay calculator rather than using a fixed certificate value.
References & Standards Cited
- ANSI N43.3-2008 General Radiation Safety for Sealed Gamma-Ray Sources
- 10 CFR 34.43 — Inspection and maintenance of radiographic exposure devices
- NIST Standard Reference Data: Atomic Weights and Half-Lives of Radionuclides
- IAEA Safety Reports Series No. 13 (1999), Radiation Protection in Industrial Radiography
Founder of NDT Connect and Atlantis NDT. 15+ years in industrial inspection across oil & gas, petrochemical, and offshore. ASNT Level III certified across five methods. Drives platform standards for the NDT Connect marketplace.