Ahalf-life is the time it takes an amount of substance to decay to one-half of its original amount. for example, the sample is one-half after the first half-life but one-quarter (i. e., one-half of one-half) after the second half-life. if the half life of uranium-235 is 700 million years, how long does it take for 10.0 grams to decay to 2.5 grams? express your answer in billions of years.

2.10 × 10⁹ yr  

Step-by-step explanation:  

The half-life of U-235 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/g  

      1                 700              ½                10.0  

      2              1400              ¼                 5.00  

      3              2100              ⅛                 2.50  

     4              2800              ¹/₁₆                 1.25  

We see that 2100 × 10⁶ yr is three half-lives, and the amount of U-235 remaining is 2.50 g.  

It takes 2.10× 10⁹ yr for the U-238 to decay to 2.50 g.