why did scientists choose the half life of an element not his quarter life or his life as the period?

Answer 1

The half life is not half the full life. If we are talking radioactivity, it is the time for half the radioactive substance to transmute into something else. The half that is left will take the same time for half of it to transmute, and so on. So you have a nearly infinite series of half lifes until all the substance has transmuted.

So the full life is not really meaningful, and the quarter life (for quarter to decay) although meaningful, is not nearly as easy to work with as the half life.

Answer 2

First of all, you need to understand the way radioactive decay works.

For any given atom of an isotope, the probability that it will begin to decay at that particular moment in time is a constant. Therefore, the more atoms you have in a sample, the faster they will decay. What you get if you plot number remaining against time is an exponential decay curve, of the form
y = a * e ** (-b * x)
where e is the base of Natural Logarithms (about 2.71828183) and a and b depend on the material.
The important thing about this graph is: it always takes the same amount of time for the amount of atoms remaining to be divided by the same number, no matter how many atoms you started with.

(Actually, in real life, it isn't a perfect exponential curve: after all, probability is descriptive, as opposed to prescriptive, and some atoms are bound to decay before or after their supposed time. But if you have plenty of atoms to consider, it actually averages out pretty well.)

The half-life is the amount of time it takes for exactly half of the atoms in the sample to decay (and so, for the measured radioactivity to halve). After two half-lives, three-quarters of the atoms will have decayed, and so on; after 10 half-lives, there will only be one atom left out of every 1024 in the original sample.

The reason why one-half is used, rather than any other fraction, is because a half is unambiguous: it doesn't matter whether you have *lost* half of what you originally had or *kept* half of what you originally had, you still end up with the same amount. Whereas if we measured, say, the "90%-life", it wouldn't be immediately obvious whether that meant the time until there were 90% of the original number of atoms *remaining*, or the time for 90% of the atoms to *decay*.

Answer 3

Truth be told, the scientifically/mathematically more useful/simple life is the mean lifetime, tau (the amount of time it takes to reduce to a fraction 1/e of the original amount) instead of the half life. But half-life is often quoted just because it is easier to explain to people. You could just as easily quote a tenth life or whatever.

Answer 4

half life works out to be ln(2)/lambda
lambda being the decay constant.
This is a nice number and I suppose it is why scientists choose to work with half life over quarter life.

Answer 5

It's just a unit of measure that is convenient to compute. Some people use feet and other people use meters but at the end they measure the same thing.

Answer 6

Half is easier to measure (exponential decay)