Question

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

Answer 1

Answer:

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.