Jun 24, 2016

$\text{2000 atoms}$

#### 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

${t}_{\text{1/2" = "1600 years}}$

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 $\text{1600}$ 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

$\text{8000 atoms" * 1/2 = "400 atoms } \to$ after $1600$ years

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

$\text{4000 atoms" * 1/2 = "2000 atoms } \to$ after $3200$ years

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