Firstly, State the formula for the half-life of a first-order reaction.

Radioactive decay follows first-order kinetics.

The half-life (t\(_{1/2}\)) for a first-order reaction is related to the rate constant (k) by the formula:

t\(_{1/2}\) = \(\frac{ln 2}{k}\)

t\(_{1/2}\) ≈ \(\frac{0.693}{k}\)

Secondly, calculate the half-life using the assumed rate constant given in the question as k = 3.85 x 10\(^{-3}\)s\(^{-1}\)

t\(_{1/2}\) = \(\frac{0.693}{3.85 x 10\(^{-3}}\)

t\(_{1/2}\) = 180 s