At radioactive equilibrium, the ratio between two atoms of radioactive elements `A` and `B` is `3.1 xx 10^(9) : 1`. If the half-life period of `A` is `2 xx 10^(10)` years, what is the half-life of `B`?

Explanation

To solve the problem, we need to find the half-life of radioactive element B given the half-life of element A and the ratio of their atoms at radioactive equilibrium.

### Step-by-Step Solution:

1. **Understand the Relationship**: At radioactive equilibrium, the ratio of the number of atoms of two radioactive elements A and B is related to their half-lives. The relationship can be expressed as:
\[ \frac{N_A}{N_B} = \frac{T_{1/2, A}}{T_{1/2, B}} \]
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