Answer to Question #181638 in Atomic and Nuclear Physics for Madi

Question

How many years has passed if only 3.125% of the original amount of U-238 remains?

Answer 1

Given

$R=0.03125R_0$

$T_{1/2}=4.5×10^9 years$

The amount of radioactivity present after time t is

$R=R_0 e^{-\frac{tln2}{t_{1/2}}}$

$0.03125R_0=R_0 e^{-\frac{tln2}{4.5×10^9 years}}$

$t=2.25 \times 10^{10} years$