Radium-226 is a radioactive element, and its decay rate is modeled by the equation R = R0e-0.000428t. How many years will it take for 100 grams of radium-226 to reduce to half its mass? 8101,6202,6905,380

It will take 1620 years.

Solution:
We calculate for the total number of particles in the 100 gram sample:
     Ro = 100 grams * 1 mol / 226 g = 0.4425 mol

We also calculate for the total number of particles when the 100 gram sample is reduced to half its mass:
     R = 100 grams/2 * 1 mol / 226 g = 0.2212 mol 

We substitute the values to the decay rate equation
     R = Ro e^-0.000428t0.2212
         = 0.4425 e^-0.000428t0.2212/0.4425
         = e^-0.000428t

Taking the natural logarithm of both sides of our equation, we can compute now for the years t:
     ln (0.2212/0.4425) = -0.000428t
     t= ln (0.2212/0.4425) / (-0.000428)
     t = 1620 years