Determining Half-lifes from a graph So I was studying for an exam I have thursday when I came across a question regarding half-life. I had previously thought that the definition of a half-life is the time it takes for the amount of material to half in its decay process. However, this question had a y-axis of Disintegration Rate, and used the same process.



They gave an answer of 8 days for the half life of this radioactive element(so they treated it as normal)

So my question is, what exactly does the half in half life represent? A halving of rate or an actual halving of decay of the nuclei?
At any time, the number of decays per reasonable$^1$ time unit is proportional to the amount of the isotope present. (This is expressed by the first-order rate equation for a one-decay process.) Therefore, it does not matter whether one looks at the amount or the number of decays. It may be easier to measure the number of decays by e.g. a Geiger counter and prefer it for that reason.

It now matters what you understand to be the rate: the number of decays per second or the percentage of nuclei decaying at any given time. The first becomes less over time, the second one is a constant for each isotope.

$^1$ You must have a reasonable number of decays within your time unit. If the half-life is long, it makes little sense to look at millisecond slices.