What percentage of a radioactive species would be found as daughter material after five half-lives?

Answer 1

Usually, 50%. That's what half-life means: the time required for 50% of the original radioisotope to undergo radioactive decay (or, alternatively, the time required for there to be a 50% chance that any given atom will have decayed). To be more specific: half of the original radioactive substance will have transformed into something else (it may still BE there, so in some sense it's "remaining", but it will be a different element or isotope). The reason for the "usually" is that it's a random process and for small numbers of atoms, the actual results may vary quite a bit from the statistically expected results. In particular, if there's only one atom, the amount remaining after one half-life period will be either 0% or 100% (50/50 chance of each).

Answer 2

After five half-lives, 3.125% of a radioisotope would be remaining in a sample.

The equation for half-life is ...

AT = A0 2(-T/H)

... where A0 is the initial activity, AT is the activity after some time T, and H is half-life in units of T.

AT = (1) 2(-5/1)

AT = 2-5

AT = 0.03125

Note: The question asked about percentage of daughter material, but that is not a valid concern because the daughter material can easily also decay and have its own half-life. It is more viable to ask how much of the parent remains, which is how I answered the question.

Answer 3

50 percent = half

Answer 4

(1/2)7 = 1/128 - less than 1%.