# Question #d1146

##### 1 Answer

#### Explanation:

You can't answer this question without knowing the **half-life** of carbon-14, so look that up before doing anything else.

You'll find it listed as

#t_"1.2" = "5730 years"#

https://en.wikipedia.org/wiki/Carbon-14

Now, a radioactive isotope's nuclear half-life tells you the time needed for **half** of an initial sample to undergo radioactive decay.

In other words, the amount of this radioactive isotope is **halved** with the passing of every half-life.

So, let's say that you start with an unknown amount of carbon-14, let's say **one half-life** passes, you will be left with

#A_ (1 xx t _"1/2") = A_0 * 1/2 = A_0/2 -> " after 5730 years"#

After **another** period of time equal to one half-life passes, you will be left with

#A_ (2 xx t_ "1/2") = A_0/2 * 1/2 = A_0/4 ->" after 2" xx "5730 years"#

This means that after

#2 xx "5730 years" = "11460 years"#

pass, the sample of carbon-14 will be down to **initial value**.

Since this is how much time passed since the plant died, you can say that **initial mass** of carbon-14 present in the plant.

Therefore, you will have

#"initial mass" = 4 xx "0.25 pg" = color(darkgreen)(ul(color(black)(1.0 color(white)(.)"pg")))#

The answer is rounded to two **sig figs**, the number of sig figs you have for the mass of carbon-14 that remains after