# Question 272dc

Jun 26, 2016

Mathematically speaking, it will take forever.
Practically speaking, it will take almost 45 billion years for 1 unit of U-238 to decay into 1 unit of Th-234.

#### Explanation:

Radioactive decay is a first-order process.

That means that it will take a certain length of time (a half-life) for half of the atoms to disappear.

It will take another half-life for half of those atoms to disappear, and so on.

You can continue for as many as many half-lives as you like, but you will always have half the remaining atoms left.

Mathematically, you can never get rid of all the atoms.

Practically speaking, we can say that the process is complete when so little material remains that it would be extremely difficult to measure.

That is probably about 10 half-lives.

The fraction of original substance remaining after 10 half lives is 1/2^10 = 0.001 color(white)(l)"or" color(white)(l)0.1 %.

That correspond to 99.9 % completion. Close enough!

The half life of U-238 is 4.468×10^9color(white)(l) "years".

Ten half lives are 44.68×10^9color(white)(l) "years"# or almost 45 billion years.

It would take almost 45 billion years for 1 unit of U-238 to decay to 1 unit of Th-234.