Answer:
The half-life of sodium-24 is approximately 12.1 hours.
Step-by-step explanation:
The half-life of a radioactive isotope is the amount of time it takes for half of a sample to decay. We can use the following equation to calculate the half-life:
N = N0 * (1/2)^(t/T)
where N is the final amount, N0 is the initial amount, t is the time elapsed, and T is the half-life.
In this case, we know that the initial amount (N0) is 208 g, the final amount (N) is 13.0 g, and the time elapsed (t) is 60.0 hours. We can solve for the half-life (T) by rearranging the equation as follows:
T = t / log2(N0/N)
T = 60.0 hours / log2(208 g / 13.0 g)
T = 60.0 hours / 4.97
T = 12.1 hours