In equilibrium for the I-135 population, how is I_0 calculated?

In the context of nuclear reactor operations and the equilibrium condition for the iodine-135 (I-135) population, the calculation of I_0 involves understanding the balance between production and decay rates of this isotope. The correct formula, which states that I_0 equals the product of the decay constants and the neutron flux across various reactions, reflects how I-135 is formed and destroyed in a nuclear reactor setting.

At equilibrium, the rate of production of I-135 from its precursors equals the rate at which it decays. The production rate can be expressed as the product of the neutron flux (φ) and the cross-section for the fission process (Σ_f), while the decay can be captured by the decay constant (γ_i). Additionally, λ_i represents the decay constant for I-135.

Thus, in the correct formula, rearranging the balance of these rates gives:

I_0 = (γ_i Σ_f φ_0) / λ_i.

This indicates that the concentration of I-135 at equilibrium depends directly on the fission reaction rates and inversely on the decay of I-135 itself. Essentially, it highlights that as the production increases through fission, the presence of more neutrons leads to more I-