A radioactive isotope of radium (Ra-226) has a half-live of 1620 years. How much of this isotope remains after three (3) half-lives?

A. 1/2
B. 1/4
C. 1/8
D. None

would this be C? please explain, thank you!

To determine how much of the radioactive isotope of radium (Ra-226) remains after three half-lives, we need to understand what a half-life represents.

The half-life is the amount of time it takes for half of the radioactive material to decay or transform into a different element. In this case, the half-life of Ra-226 is 1620 years, which means that after 1620 years, half of the Ra-226 atoms will have decayed.

To calculate the amount remaining after three half-lives, we need to halve the remaining amount after each half-life.

Let's start with an initial amount of 100 units of Ra-226. After the first half-life (1620 years), half of the substance will decay, leaving 50 units. After the second half-life (another 1620 years), half of the remaining 50 units will decay, leaving 25 units. Finally, after the third half-life (another 1620 years), half of the remaining 25 units will decay, leaving 12.5 units.

So after three half-lives, 12.5 units of Ra-226 remain, which is 1/8th (or 1/2 * 1/2 * 1/2) of the initial amount. This means the correct answer is option C.