Uranium-235 has a half-life of 7.038×108 years.(i) Determine the time required for the mass of 235U in a sample originally containing 1.000 g of 235U to decrease to 0.125 g.

To solve this problem, we need to understand the concept of half-life. The half-life of a radioactive substance is the time it takes for half of the substance to decay.

Given that the half-life of Uranium-235 is 7.038 x 10^8 years, we can use this information to determine how long it will take for the mass of Uranium-235 to decrease from 1.000 g to 0.125 g.

1. First, we need to determine how many half-lives it takes for 1.000 g to decrease to 0.125 g. Since each half-life reduces the substance by half, we can calculate this as follows:

   • After 1 half-life, the mass would be 0.500 g.
   • After 2 half-lives, the mass would be 0.250 g.
   • After 3 half-lives, the mass would be 0.125 g.

So, it takes 3 half-lives for the mass to decrease from 1.000 g to 0.125 g.

2. Next, we multiply the number of half-lives by the length of each half-life to find the total time:

   • Time = number of half-lives x length of each half-life
   • Time = 3 x 7.038 x 10^8 years
   • Time = 2.1114 x 10^9 years

So, it would take approximately 2.1114 x 10^9 years for the mass of Uranium-235 in a sample originally containing 1.000 g to decrease to 0.125 g.