24,951,485,881.209
Bq
0.674364
Ci
37,180,000,000
Bq
67.11%
24,951,485,881.209
Bq
0.674364
Ci
37,180,000,000
Bq
67.11%
The Neutron Activation Calculator computes the radioactivity induced in a target material when bombarded with neutrons in a reactor or neutron source. Neutron activation is the process by which a stable nucleus captures a neutron and becomes radioactive, and it is the basis for Neutron Activation Analysis (NAA), one of the most sensitive elemental analysis techniques, as well as for radioisotope production in nuclear medicine and industry.
The induced activity depends on four factors: the number of target atoms, the neutron capture cross section, the neutron flux, and the irradiation time relative to the product half-life. The activity builds up exponentially toward a saturation value where the rate of production equals the rate of decay. This calculator implements the standard activation equation $$A = N\sigma\phi(1 - e^{-\lambda t})$$ used in reactor physics and analytical chemistry.
The fundamental neutron activation equation balances production and decay:
$$A(t) = N \sigma \phi \left(1 - e^{-\lambda t_{irr}}\right)$$
where:
$$N$$ = number of target atoms
$$\sigma$$ = thermal neutron capture cross section (cm², converted from barns)
$$\phi$$ = neutron flux (neutrons/cm²/s)
$$\lambda = \ln(2)/t_{1/2}$$ = decay constant of the product
$$t_{irr}$$ = irradiation time
The saturation activity (maximum achievable) is:
$$A_{\infty} = N \sigma \phi$$
reached asymptotically as $$t_{irr} \rightarrow \infty$$. In practice, after 5-7 half-lives, the activity reaches >98% of saturation, and further irradiation provides diminishing returns. This assumes the target is not significantly depleted (thin target approximation) and the neutron flux remains constant.
Induced Activity (Bq, Ci) is the radioactivity of the irradiated sample at the end of bombardment. Saturation Activity is the theoretical maximum activity achievable with infinite irradiation time for these conditions. The Fraction of Saturation shows how close you are to maximum — irradiating for one half-life gives 50%, two half-lives gives 75%, and so on. For isotope production, the optimal irradiation time balances activity yield against reactor time cost, typically 1-3 half-lives.
Inputs
Results
Irradiating Na-23 for 24 hours (1.6 half-lives of Na-24) achieves ~67% of saturation activity. Na-24 (t½ = 15h) is widely used in NAA and flow tracing.
Inputs
Results
After 2 years (~0.38 half-lives), Co-60 production reaches ~23% of saturation. Co-60 sources for radiotherapy typically require years of reactor irradiation due to the long half-life.
Neutron activation occurs when a stable nucleus absorbs a neutron and becomes a radioactive isotope. The target nucleus (Z, A) captures a neutron to form (Z, A+1), which is typically radioactive and decays by beta emission. The induced radioactivity is proportional to the neutron flux, cross section, target atoms, and irradiation time.
NAA is an analytical technique that identifies and quantifies elements by measuring the characteristic gamma rays from neutron-activated isotopes. It can detect elements at parts-per-billion sensitivity without destroying the sample. NAA is used in archaeology, forensics, geology, environmental science, and materials science.
Saturation activity ($$A_\infty = N\sigma\phi$$) is the maximum activity achievable when irradiation time is much longer than the product half-life. At saturation, the rate of radioactive atom production equals the rate of decay. Beyond ~5 half-lives of irradiation, the activity is within 3% of saturation.
The optimal irradiation time depends on the purpose. For NAA, 1-3 half-lives provides a good balance of activity and measurement time. For isotope production, economic factors (reactor time cost) are weighed against activity yield. Each additional half-life of irradiation adds progressively less activity (50% of remaining deficit).
After irradiation ends, the activity decays exponentially: $$A(t_d) = A(t_{irr}) \cdot e^{-\lambda t_d}$$ where $$t_d$$ is the decay time after irradiation. The total activity at any time involves the irradiation buildup factor times the post-irradiation decay factor.
Research reactors typically provide thermal neutron fluxes of 10¹² to 10¹⁴ n/cm²/s. Power reactors reach 10¹³ to 10¹⁴ n/cm²/s. The highest fluxes (~10¹⁵ n/cm²/s) are found in dedicated isotope production facilities and high-flux reactors like the Institut Laue-Langevin (ILL) reactor.
No, this is the thin target (or low burnup) approximation where the number of target atoms N is assumed constant. For very high fluxes, long irradiations, or high cross sections, target depletion becomes significant and the full equation $$A = \frac{N_0 \sigma \phi}{\lambda - \sigma\phi}(e^{-\sigma\phi t} - e^{-\lambda t})$$ should be used.
Neutron flux is measured using activation monitors (foils of gold, cobalt, or other materials with well-known cross sections), fission chambers, BF₃ proportional counters, or He-3 detectors. Self-powered neutron detectors (SPNDs) provide continuous flux monitoring in reactors.
Major isotopes include Mo-99 (parent of Tc-99m for SPECT imaging), Co-60 (radiotherapy), I-131 (thyroid treatment), Lu-177 (targeted radionuclide therapy), Ir-192 (brachytherapy), and Sm-153 (bone pain palliation). Mo-99 production alone accounts for a significant fraction of research reactor neutron usage worldwide.
Thermal neutrons (~0.025 eV) have the highest capture cross sections for most isotopes, following the 1/v law. Fast neutrons (>1 MeV) can induce threshold reactions like (n,p), (n,α), and (n,2n) that thermal neutrons cannot. Different reaction channels provide complementary analytical information in NAA.
Roboculator Team
The Roboculator Team explains calculations, planning tools, and practical formulas in clear language for real-life situations.
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