Question

If the half life of a radioactive isotope is 5000 years, how much of the radioactive isotope in a specimen will be left after 10000

Answer 1

Half life is the time taken by a radioactive isotope to decay by half its original mass. In this case, the halflife of the radioactive isotope is 5000 years. 
Initially the mass is 100 %; thus the mass that will be left will be given by;
New mass = Original mass × (1/2)^n where n is the number of half lives; 
  n = 10000/5000 = 2
New mass = 100% ×(1/2)^2
                 = 100 % × 1/4 
                 = 25%
Therefore; the mass left after 10000 years is 25% or 1/4 of the original mass.