\[A=n\sigma\phi(1-e^{-\lambda t})\]
Variables
Aactivity (Bq)
ntarget atom density (atoms)
sigma[σ]microscopic cross section (m²)
phi[Φ]neutron flux (neutrons/m²·s)
lambda[λ]decay constant (1/s)
tirradiation time (s)
Description
What is this formula?
This formula calculates the radioactive activity generated when a material is exposed to a neutron flux. The activity grows during irradiation and approaches a saturation value over time.
When to use it
Use this formula in neutron activation analysis, isotope production, nuclear reactor calculations, and radiation source generation.
Example
Given:
n=5×10^20 atoms
σ=4×10^-28 m²
Φ=2×10^15 neutrons/m²·s
λ=0.0002 1/s
t=3600 s
Formula:
A=nσΦ(1-e^(-λt))
Substitution:
A=(5×10^20)(4×10^-28)(2×10^15)(1-e^(-(0.0002)(3600)))
Result:
A=4.11×10^8 Bq
Applications
- Neutron activation analysis
- Medical isotope production
- Reactor calculations
- Nuclear laboratories
- Radiation source design