# Question 46693

Nov 22, 2015

$\text{0.0597 g}$

#### 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

$\textcolor{b l u e}{A = {A}_{0} \cdot \frac{1}{2} ^ n} \text{ }$, 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 $\text{1.00 g}$. 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

$\textcolor{b l u e}{n = \text{total time"/"half-life}}$

In this case, you will have

$n = \left(50.0 \textcolor{red}{\cancel{\textcolor{b l a c k}{\text{years"))))/(12.3color(red)(cancel(color(black)("years}}}}\right)$

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.