What is the half-life of the first-order decay with k = 0.231 h^-1?

• A. 3.0 h
• B. 0.231 h
• C. 0.693 h
• D. 1.0 h

Answer: (A)

In first-order decay, the half-life t1/2 is determined by how fast the quantity decays, independent of how much you start with. The relationship is t1/2 = ln 2 / k, because setting N = N0/2 in N = N0 e^{-kt} leads to e^{-k t1/2} = 1/2 and thus k t1/2 = ln 2.

Plugging in k = 0.231 h^-1 gives t1/2 = 0.693 / 0.231 h ≈ 3.0 h. So the half-life is 3.0 hours. The rate constant itself is 0.231 h^-1, not the half-life; the number 0.693 h would correspond to a different k (specifically k = 0.693 h^-1), and 1.0 h does not satisfy the equation.