Question

What is meant by ‘half-life' of a radioactive element? what percentage of a given mass of a radioactive substance will be left undecayed after four half lives?

Answer 1

By definition, a half-life is a time period after which a substance (radioactive in this case) has a 50% chance to have decayed completely, however by observing we see that, after a half life 50% of the original quantity of the substance has decayed.

So after each half-life the amount of substance halves.

After 1 half life, remaining amount is 50%
After 2 half lives, remaining amount is 25%
After 3 half lives, remaining amount is 12.5%

And so on.

A good to way find out what fraction of original amount remains after n half lives is this formula
${ (\frac{1}{2} )}^{n}$
where n is the number of half-lives.


So after 4 half-lives we can say that (1/16) th of the original amount remains which is 6.25%