Question

The half life of radium is 1590 yrs. how long will it take to 1 gm of element to loose 0.1gm

Answer 1

that means that 90% remains, so

(1/2)^(t/1590) = 9/10
t = 241.7 years

Answer 2

Steve's calculation is correct. It is worth noting that if you had an actual 1 gram block of Radium-226, its mass would NOT be reduced all the way to 0.9 grams after 241.7 years. Radium-226 decays by alpha emission to Radon-222, which goes quickly through a sequence of further decay ending with stable Lead-206, much of which would still be trapped within the metal block and would contribute to its remaining mass.