Let's say we start with 2.2lbs of uranium. If the half-line of U-235 is 703.8 million years, how much uranium will we have after 2,815 million years

0.14 lb

Explanation:

The half-life of U-235 (703.8 * 10⁶ yr) is the time it takes for half the U to decay.

After one half-life, half (50 %) of the original amount will remain.

After a second half-life, half of that amount (25 %) will remain, and so on.

We can construct a table as follows:

No. of Fraction Amount

half-lives t / (yr * 10⁶) remaining remaining/lb

1 703.8 ½ 1.1

2 1408 ¼ 0.55

3 2111 ⅛ 0.28

4 2815 ¹/₁₆ 0.14

We see that 2815 * 10⁶ yr is four half-lives, and the amount of U-235 remaining is 0.14 lb.