# Question #1f1d8

##### 1 Answer

#### Explanation:

You can't provide a definite answer here because you don't have any information about the **half-life** of plutonium-239, but you can work your way to an answer that depends exclusively on the half-life of the nuclide.

So, you know that radioactive decay can be modeled using the equation

#A_t = A_0 * (1/2)^(t/t_"1/2")#

Here

#A_t# is the mass of the nuclide thatremains undecayedafter a given period of time#t# #A_0# is theinitial massof the nuclide#t_"1/2"# is thehalf-lifeof the nuclide

Now, in order for the nuclide to decay to

#A_t = 12/100 * A_0#

#A_t = 3/25 * A_0#

This basically means that after an unknown period of time

Plug this back into the equation to get

#3/25 * color(red)(cancel(color(black)(A_0))) = color(red)(cancel(color(black)(A_0))) * (1/2)^(t/t_"1/2")#

#3/25 = (1/2)^(t/t_"1/2")#

Next, take the log base

#log(3/25) = log[ (1/2)^(t/t_"1/2")]#

This will get you

#t/t_"1/2" * log(1/2) = log(3/25)#

Rearrange to solve for

#t = log(3/25)/log(1/2) * t_"1/2"#

#t = 3.06 * t_"1/2"#

Now, the half-life of the nuclide tells you the amount of time needed for exactly **half** of the sample to undergo radioactive decay.

This means that you can say that your sample of plutonium-239 will decay to **half-lives** pass.

At this point, all you have to do is to look up the half-life of plutonium-239--you can find it **here**--and use it to find the value of **sig figs**.