# Question #3890e

##### 1 Answer

#### Explanation:

Your go-to equation when it comes to calculating the amount of a radioactive sample that remains after the passing of a certain period of time looks like this

As you know, the nuclear half-life of a radioactive substance is defined as the time needed for **half** of the atoms of that sample to undergo radioactive decay.

In other words, the nuclear half-life tells you how much time must before before a sample of a radioactive substance is reduced to **half** of its original mass.

In your case, the half-life of plutonium is known to

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

#n = (5.0 * 10^3color(red)(cancel(color(black)("years"))))/(2.4 * 10^4color(red)(cancel(color(black)("years")))) = 25/12 * 10^(-1) = 5/24#

This means that the amount of plutonium that remains *undecayed* after that much time will be

#A = "2.0 g" * 1/2^(5/24) = color(green)("1.7 g")#