The half-life for the radioactive decay of U-238 is 4.5 billion years and is independent of initial concentration.

Question

a) How long will it take for 10% of the U-238 atoms in a sample of U- 238 to decay?

b)If a sample of U-238 initially contained 1.9×1018 atoms when the universe was formed 13.8 billion years ago, how many U-238 atoms will it contain today?

Answer 1

k = 0.693/t_1/2
Then
ln(No/N) = kt
I would call No = 100
Then N = 90(after 10 have decayed--which is 10%)
k from above. Solve for t in years.

b.
Same procedure. No = atoms you started with. N = atoms remaining.