How long will it take for 20% of the {\rm U}-238 atoms in a sample of {\rm U}-238 to decay?

That will depend on the half life of Uranium-238. Google half-life formula, and you'll surely find the formula used to calculate it. If you don't know how to use it, post back.

The percentage of atoms that remain as U238 (not yet decayed) at time t is: 0.5^{(\frac t H )}


where t = time and H = half life. The half-life of U238 is about 4.47 Billion years. So you want to solve for t:


0.80 = 0.5^{(\frac t {4.47 \ BY} ) }


Take the log of both sides and rearrange to find t.