The activity of a radioactive sample is the number of nuclear disintegrations per second, which is equal to the first order rate constant times the number of radioactive nuclei present. The fundamental unit of radioactivity is the Curie, where one Curie represents exactly 3.70 x 1010 disintegrations per second. This decay rate is equivalent to that of 1.0 g of radium-226.
a) Calculate the rate constant and half- life for the radium decay.
b) Starting with 1.0 g of the radium sample, what is the activity after 500 years? The molar mass of ra-226 is 226.03 g/mol.