Answer to Question #347541 in Physics for Loie

Question

How long would it take 4.0 x 10²⁰ atoms to decay to 1.0 x 10¹⁹ atoms if their half-life was 14.7 years?

Answer 1

$$N=N_02^{-t/t_{1/2}}$$ $$1.0*10^{19}=4.0*10^{20}*2^{-t/14.7\:\rm yrs}$$ $$t=-14.7*\log_2(1.0*10^{19}/4.0*10^{20})=78\:\rm yrs$$