A radioactive substance used in nuclear weapons decays at the rate of $2.9 \%$ per year. Calculate the half-life of the radioactive substance.

Step 1 ：We are given that a radioactive substance used in nuclear weapons decays at the rate of 2.9% per year. We are asked to calculate the half-life of the radioactive substance.

Step 2 ：The half-life of a substance is the time it takes for half of the substance to decay. In this case, we are given the decay rate per year, so we can use the formula for exponential decay to solve for the half-life.

Step 3 ：The formula for exponential decay is: \[ N = N_0 * e^{-kt} \] where: \(N\) is the final amount of the substance, \(N_0\) is the initial amount of the substance, \(k\) is the decay constant, and \(t\) is time.

Step 4 ：In this case, we know that \(N = 0.5 * N_0\) (since we're looking for the half-life), and \(k = 0.029\) (since the decay rate is 2.9% per year). We can plug these values into the formula and solve for \(t\).

Step 5 ：By solving the equation, we find that the half-life of the radioactive substance is approximately 23.9 years.

Step 6 ：Final Answer: The half-life of the radioactive substance is approximately \(\boxed{23.9}\) years.