Question

A new element (Trumpium, atomic number 120) was found to exist on Mars! (It really is the greatest element there is, no other element is as great as Trumpium) However when brought back to Earth, it was found to rapidly decay with a half-life of only 0.01 seconds! What is the rate constant (k) for this decay on Earth?

Answer 1

The rate constant (k) for the decay of Trumpium can be calculated using the first-order rate law equation, which is given by ln(N/N0) = -kt, where N is the amount of Trumpium remaining after time t, N0 is the initial amount of Trumpium, and ln is the natural logarithm. Since the half-life of Trumpium is 0.01 seconds, we can use the half-life equation for first-order reactions, which is t1/2 = ln(2)/k, to find the value of k. Rearranging this equation, we get k = ln(2)/t1/2. Substituting t1/2 = 0.01 seconds, we get k = ln(2)/0.01 seconds = 69.31 s^-1. Therefore, the rate constant for the decay of Trumpium on Earth is 69.31 s^-1.