If we start with 8000 atoms of radium-226, how much would remain after 3,200 years?

1 Answer
Jun 24, 2016

Answer:

#"2000 atoms"#

Explanation:

The problem doesn't provide you with the nuclear half-life of the radium-226 isotope, so you're going to have to do a bit of research on that.

You can find this isotope's half-life listed as

#t_"1/2" = "1600 years"#

https://en.wikipedia.org/wiki/Isotopes_of_radium

So, the half-life of a radioactive nuclide tells you how much time must pass in order for half of an initial sample of said nuclide to undergo radioactive decay.

In your case, the half-life of radium-226 tells you that a sample of this nuclide will need #"1600"# years to be reduced to half of its initial size.

Your starting sample contains #8000# atoms of radium-226, so you can say that after one half-life passes, you will be left with

#"8000 atoms" * 1/2 = "400 atoms " -># after #1600# years

How about after two half-lives pass? The remaining sample will be halved again

#"4000 atoms" * 1/2 = "2000 atoms " -># after #3200# years

Therefore, your initial sample of radium-226 will be down to

#"no. of atoms that remain undecayed" = color(green)(|bar(ul(color(white)(a/a)color(black)("2000 atoms")color(white)(a/a)|)))#