Answer to Question #18263 in Atomic and Nuclear Physics for Kami

Question

A radioactive nucleus has a half-life of 5x10^8 years. Assuming that a sample of rock solidified right after the solar system formed, approximately what fraction of the radioactive element should be left in the rock today?

Answer 1

if we assume that age of solar system is approximately4.5x10^8 years, then law of radioactive decay tells us
N=N_0*2^{-t/T_{1/2}} = N_0*2^{-4.5/5} = N_0 = 0.534.
Hence, it will left only 53.4% of primordial amount