Question #46693

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.