Question

Question #46693

Answer 1

`"0.0597 g"`

Explanation:

The thing to remember about nuclear half-life calculations is that on original sample of a radioactive substance will be halved with every passing of a half-life.

Mathematically, you can write this as

`color(blue)(A = A_0 * 1/2^n)" "`, where

`A` - the amount of the radioactive substance that remains after the passing of `n` half-lives
`A_0` - the initial mass of the sample
`n` - the number of half-lives that passed

Keep in mind, `n` does not have to be a whole number. The above equation is valid whether or not a whole number of half-lives pass.

In your case, the mass of the original sample is `"1.00 g"`. The half-life of tritium is said to be equal to `12.3` years. To get the value of `n`, divide the total time that passed by the half-life of the isotope

`color(blue)(n = "total time"/"half-life")`

In this case, you will have

`n = (50.0color(red)(cancel(color(black)("years"))))/(12.3color(red)(cancel(color(black)("years"))))`

This means that you'll be left with

`A = "1.00 g" * 1/2^(50.0/12.3) = color(green)("0.0597 g tritium")`

The answer is rounded to three sig figs.