# Question #272dc

##### 1 Answer

#### Answer:

**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:

**The mathematical answer**

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.

**The practical answer**

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

That correspond to 99.9 % completion. Close enough!

The half life of U-238 is

Ten half lives are

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