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

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.