Neutron activation analysis calculator online || NuclearApplication.com

In this article, you can do calculation for yield or activity of Radioisotopes after neutron activation. Neutron activation equation is shown below. 

Neutron activation analysis application plays a significant role in various fields.

Neutron activation analysis in forensic science plays a key role to investigate a crime incident. 

Let's see the Detailed Breakdown of the Activation Equation

The equation provided here is fundamental in neutron activation analysis, radioisotope production, and nuclear reactor physics. Let’s dissect it thoroughly:

$$A\text{(Bq)}=N\cdot \sigma \cdot \mathrm{\Phi }\cdot (1-e^{-\lambda \cdot t_{\text{irr}}})$$

1. Variables and Their Meanings

Symbol	Description	Units (SI)
$A$	Activity of the produced radioactive isotope	Becquerels (Bq)
$N$	Number of target nuclei available for irradiation	Unit less (number of atoms)
$\sigma$	Microscopic cross-section for the nuclear reaction (e.g., neutron capture)	m² (or barns, 1 barn = 10⁻²⁸ m²)
$\mathrm{\Phi }$	Particle flux (neutrons) incident on the target	Particles/(m²·s)
$\lambda$	Decay constant of the produced isotope ($\lambda =\ln (2)\mathrm{/}{t}_{1\mathrm{/}2}$	s⁻¹
$t_{\text{irr}}$	Irradiation time	Seconds (s)

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2. Physical Interpretation

$$

$N\cdot \sigma \cdot \mathrm{\Phi }$ = Production rate of radioactive isotopes (atoms produced per second). 

$\mathrm{<span> \; </span>N}\cdot \sigma$ = Total cross-sectional area of all target nuclei exposed to the flux.

    Multiplying by $\mathrm{\Phi }$ gives the interaction rate.

$$

$(1-e^{-\lambda \cdot t_{\text{irr}}})$ = Saturation factor

    Accounts for the fact that as radioactive atoms are produced, they also decay.

        At short times ($t_{\text{irr}}\ll t_{1\mathrm{/}2}$), the activity grows linearly: $A\approx N\cdot \sigma \cdot \mathrm{\Phi }\cdot \lambda \cdot t_{\text{irr}}$

${}_{}$At long times ($t_{\text{irr}}\gg t_{1\mathrm{/}2}$), saturation occurs: $A_{\text{sat}}=N\cdot \sigma \cdot \mathrm{\Phi }$

Example Calculation: Producing Indium-114

Goal: Calculate the activity of In-114 produced after irradiating 1 gram of pure In₂O₃ in a nuclear reactor for 1 min.

Input parameters are as follows

Compound's Molecular Weight (MW): 277.64 g/mol

Number of Atoms of Interest (n): 2

Atomic Weight of Element (AW): 114.818 g/mol

Weight of Compound taken for irradiation (x): 1 g

% Abundance (θ): 4.28%

Cross Section (σ): 1 barn

Flux (Φ): 1.5 × 1012 n.cm-2.s-1

Half Life (t₁/₂): 71.9 s

Irradiation Time (tᵢᵣᵣ): 1 min 

Calculation Steps:

1. Absolute Abundance: θ = % Abundance / 100 = 4.28 / 100 = 0.0428

2. Weight of Element: w = (n * AW / MW) * x = (2 * 114.818 / 277.64) * 1 = 0.827100 g

3. Number of Atoms: N = (w / AW) * θ * Nₐ = (0.827100 / 114.818) * 0.0428 * 6.02214076e23 = 1.8567e+20

4. Decay Constant: λ = ln(2) / t₁/₂ = 0.693 / 71.9 s = 9.6404e-3 s⁻¹

5. Activity: A = N * σ * Φ * (1 - e^(-λ * tᵢᵣᵣ)) = 1.8567e+20 * 1.0000e-24 * 1.5000e+12 * (1 - e^(-9.6404e-3 * 60)) = 1.2233e+8 Bq

Final Results:

Activity:

    122325126.16 Bq
    122325126160.59 mBq
    122.33 MBq
    0.12 GBq
    3306084.49 nCi
    3306.08 µCi
    3.31 mCi
    0.00 Ci

Now you can try the calculator yourself

Nuclear Activity Calculator

Compound's Molecular Weight (MW, g/mol): Number of Atoms of Interest (n): Atomic Weight of Element (AW, g/mol): Weight of Compound (x, g): % Abundance (θ, 0% to 100%): Cross Section (σ):

barn nb µb mb

Flux (Φ):

× 10^ n.cm⁻².s⁻¹ n.m⁻².s⁻¹

Half Life (t₁/₂):

seconds minutes hours days months years

Irradiation Time (tᵢᵣᵣ):

seconds minutes hours days months years

 

Reference

1. Nuclear and Radiochemistry 3rd Edition by Gerhart Friedlander , Joseph W. Kennedy , Edward S. Macias , Julian M. Miller.