The half life of radium 226 is 1602 years. if you have 500 grams of radium today how many grams would have been present 9612 years ago?

Half life is the time taken by a radio active isotope to reduce by half of its original amount. Radium-226 has a half life of 1602 years meaning that it would take 1602 years for a mass of radium to reduce by half.
Number of half lives in 9612 years = 9612/1602 = 6 half lives
New mass = Original mass x (1/2)n where n is the number of half lives.
Therefore, New mass= 500 x (1/2)∧6
                                  = 500 x 0.015625
                                  = 7.8125 g
Hence the mass of radium after 9612 years will be 7.8125 grams.