What is the total number of years that must pass before only 25.00 grams of an original 100.0-gram sample of C-14 remains unchanged?

(1) 2,865 y (3) 11,460 y

(2) 5,730 y (4) 17,190 y

The answer is (3) 11,460 y. For this problem, you must know that the half life of C-14 is 5740 y and that nuclear decay processes are first order reactions (which means that the half life remains constant). For 25.00g to be left of a 100.0g sample, two half life must have elapsed (100*0.5*0.5=25). Each half life is 5730 y, so the total time elapsed is 5730 * 2 = 11,460 y.