# Question #e121a

##### 2 Answers

You will be left with

#### Explanation:

A radioactive isotope's nuclear half-life tells you how much time must pass before the **half** of the original sample undergoes decay.

In your case, the half-life of iodine-131 is **8 days**. This means that any sample of iodine-131 that undergoes decay will be **halved** after 8 days, **halved again** after another 8 days, **halved again** after another 8 days, and so on.

You know that the fuel rods are stored underwater for **56 days**. You can use this value to determine *how many half-lives* will pass.

Plug in your values to get

So, if the initial amount gets halved with every passing half-life, you can write

In your case, you have

This means that the fraction remaining after 56 days will be

1/128 remains

#### Explanation:

The first thing to do is count how many half lives have elapsed.

The half life (

You can see that 56 days is 7 half lives since 56/8 = 7

To get the fraction remaining we need to x by 1/2 seven times:

1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 = 1/128

If you don't get nice numbers like this you can use the equation for radioactive decay:

We get the decay constant from the half life:

Taking natural logs

From which

To compare this with the other method we can check the value of 1/128 = 0.00781 so that agrees quite nicely.