What is the relationship between the rate constant and the half-life for nuclear decay?

Question

Quizplus · Accepted Answer

The relationship between the rate constant (k) and the half-life (t1/2) for nuclear decay is given by the equation k = ln(2)/t1/2. This equation is derived from the exponential decay equation A = A0e-kt, where A is the amount of radioactive material left after time t, and A0 is the initial amount. The half-life is the time it takes for half of the initial amount to decay, which can be solved for by setting A = 1/2A0 and t = t1/2. Substituting these values into the exponential decay equation and solving for k yields k = ln(1/2)/t1/2 = ln(2)/t1/2.

What Is the Relationship Between the Rate Constant and the Half-Life