Neutron Activation Calculator

Calculate induced radioactivity from neutron irradiation using activation analysis.

Research reactor: 10¹²-10¹⁴
1 barn=10⁻²⁴ cm², Na-23: 0.53b, Au-197: 98.7b
Au: 197
Au-198: 64.8hr
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Why Activity Saturates

During irradiation, nuclei are being created by neutron capture and destroyed by decay simultaneously. Production is constant, but decay grows as activity accumulates — so activity climbs toward a ceiling where the two rates balance.

A = φσN(1 − e−λt)
Irradiation timeFraction of saturationPractical note
1 half-life50%Useful
2 half-lives75%Good return
3 half-lives87.5%Diminishing
5 half-lives96.9%Practical maximum
10 half-lives99.9%Reactor time wasted

Irradiating beyond about three half-lives gives little additional activity for substantial reactor time. This is why irradiation schedules are set by the product's half-life rather than by convenience.

Why NAA Is So Sensitive

Neutron activation analysis detects elements at parts-per-billion levels because it measures gamma rays of characteristic energy from the activated nuclei. Each isotope emits at a specific energy, so identification and quantification happen together with very low background.

AdvantageWhy it matters
Non-destructiveSample survives — used on artefacts and forensic evidence
Matrix independentNeutrons penetrate; no dissolution or digestion needed
Multi-elementMany elements measured in one irradiation
Very low detection limitsParts per billion for many elements

The main constraints are access to a reactor and the half-life of the product. Very short-lived products must be counted immediately, while long-lived ones require cooling time before the sample can be handled safely.

Worked Examples

Example 1: Gold foil: 10mg, φ=1e13, σ=98.7b, t=24hr, t½=64.8hr
A_sat=phi×σ×N, fraction=1-e^(-t×ln2/t½)
Result: A≈2.1×10⁷ Bq after 24hr irradiation
Au-198 used for lymph node mapping
Example 2: Na in food sample: σ=0.53b, 1mg Na, t=1hr, t½=15hr
Na-24 activity after 1hr irradiation
Result: Small fraction of saturation — need longer irradiation
NAA for food safety analysis
Example 3: Choosing irradiation time
Product half-life 15 hours, reactor time limited
Result: 3 half-lives gives 87.5%
Beyond 45 hours the return falls sharply. Doubling to 90 hours would add only about 11 percentage points.
Example 4: Why NAA suits archaeology
Non-destructive, matrix independent, ppb sensitivity
Result: Artefacts survive analysis
Trace element fingerprints identify the geological source of pottery clay or obsidian without damaging the object.

Common Mistakes

⚠️
Irradiating far beyond three half-lives

Activity is already at 87.5% of saturation and gains slow sharply. Longer irradiation mostly consumes reactor time without benefit.

⚠️
Forgetting decay during counting

Short-lived products decay measurably between the end of irradiation and measurement. Decay correction to a reference time is essential.

⚠️
Ignoring isotopic abundance

Only the specific target isotope activates. The natural abundance of that isotope must be included when converting sample mass to target nuclei.

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Assuming all elements activate usefully

Some have tiny cross-sections or produce products with inconvenient half-lives. NAA is excellent for many elements and poor for others.

Frequently Asked Questions

Why use NAA for chemical analysis?
Elemental analysis without chemical dissolution. Detect ppb-ppt concentrations non-destructively. No blank contamination. Multi-element simultaneously by gamma spectroscopy. Used for art authentication, geological samples, environmental monitoring, forensics.
Saturation activity concept?
At saturation, production rate = decay rate: φσN = λA_sat. This is maximum achievable activity regardless of irradiation time. Approach saturation: 50% at 1 half-life, 87.5% at 3, 99.9% at 10. Beyond 10 t½, more irradiation doesn't help.
Why does activity reach saturation?
Because production by neutron capture is constant while decay increases with accumulated activity. The two balance at the saturation value.
How long should I irradiate?
Typically two to three half-lives of the product, giving 75–87.5% of saturation. Beyond that the additional gain rarely justifies the reactor time.
Why is neutron activation analysis so sensitive?
It measures gamma rays of characteristic energy against very low background, giving parts-per-billion detection for many elements without chemical separation.
Is the sample destroyed?
No, which is a major advantage. The technique is used on archaeological artefacts and forensic evidence where the sample must be preserved.

Formula Explorer connections

Interpretation: This relationship connects isotopic composition, decay, radiation, mass defect or nuclear energy to a measurable quantity. Assumption: Use the correct nuclide, decay constant, branching behavior and time units. Radiation estimates also depend on geometry, shielding and detector response.

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