Half-Life is also a scientific term. It's the time needed for something to be reduced to half its original value.
In medicine, when someone is given a dose of a drug (for cancer, pain, infection or whatever), the concentration of that drug peaks, then starts falling off. The human body removes foreign substances by several mechanisms, including excretion and absorption. Due to the action of the removal mechanisms, eventually the patient has only half as much medicine in their body.
This is the "Biological Half-Life" - The time it takes for half of the medicine to be removed from the patient. After a few Biological half-lives, another dose of medicine will be needed to keep the drug's concentration at the desired level. This is the basis for timing and dosing of medicines.
That's medicine (and we will get back to that). But I like to talk about radioactive stuff. Stuff that glows... Like a vintage Radium watch.
Half-life *also* applies to radioactive substances (thus the name for the famous video game). "Half-Life", in this sense, is the amount of time it takes for a one-half of a radioactive substance to decay into something else. Like many other forces of nature, the half-life of a radioactive substance is fixed. Nothing we can do changes how fast or slow something decays (with a few minor exceptions)
Radioactive decay is governed by the weak force, and the process of decay is similar in some respects to electrons becoming excited, then eventually returning to ground state (lowest entropy) by emitting light (like in a neon sign or LED light). The nucleus, being bound with significantly stronger forces, emits energy millions of times more powerful than light. Image below, courtesy of Wikipedia
The mathematical expression for determining the remaining radioactive quantity after a given time are any of these three formulae. Which equation you use depends on what information you have available. With these equations it's not too difficult to determine how much bad stuff remains.
N(t) = No (1/2)(t/t1/2)
N(t) = No e-(t/τ)
N(t) = Nο e-λt
N(t) is how much radioactive stuff remains after a given time
No is how much radioactive stuff you initially started with
t = elapsed time
t1/2 = half-life of the radioactive stuff
τ= mean lifetime of a radioactive substance
e= Euler's number (~2.73). This is a naturally occurring number, similar to Pi.
λ= lambda, the decay constant of a radioactive substance.
Linked here is a practical example of using one of the formulas to figure it out!
The relationship between Half-Life and Lambda (λ) is t1/2=ln2/λ
Cool enough - in the Half-Life game, you were supposed to try to find "Lambda team" or some such. It's also the game logo.
Back though to our understanding of half-life. Knowing the math, we can make a table of how things fade over time, without ever really reaching zero...
Half-Lives Elapsed
|
Fraction Remaining
|
Percentage Remaining
|
0
|
1/1
|
100%
|
1
|
1/2
|
50%
|
2
|
1/4
|
25%
|
3
|
1/8
|
12.5%
|
4
|
1/16
|
6.25%
|
5
|
1/32
|
3.125%
|
6
|
1/64
|
1.563%
|
7
|
1/128
|
0.781%
|
The length of the half-life determines how quickly a substance decays away. If the substance has a very short half-life, it won't be around very long at all.
For example, Nitrogen-16: This is created in a nuclear reactor in large quantities by the n,p reaction with Oxygen-16 in the coolant/moderator. The half-life of N-16 is 7.13 seconds, and it emits a sizzling hot 6 MeV gamma, so this stuff is dangerous. After the reactor is shut down and neutrons are no longer available, the N-16 decays away after just a few minutes, and thereafter presents no hazard.
At the other extreme is naturally-occurring U-238. U-238 has a half-life of over 4 billion years! With this long half-life, there is primordial radioactive Uranium decaying underfoot to this day.
One of my pet peeves is when people say stuff like, "It will be radioactive for thousands of years!!! OMG". Yep, and take a look at U-238. It's radioactive for billions of years. It's also found in the soil in which we grow our food!!! OMG we are all going to die... or maybe not.
If the half-life is extremely long, it's *almost* as though it were not radioactive at all. Very little of the substance will decay in your brief lifetime, and so the odds of it harming you are pretty low. The real issue is materials with a medium-length half-life - particularly if they have the ability to bio-absorb and/or climb up the food chain. Radioactive materials that are not readily absorbed by the body (Cobalt 60, for example), will simply pass through if ingested, although of course they will irradiate the digestive system, which is to be avoided :)
During operation, a nuclear reactor produces over 300 different radioactive isotopes, of which only three are of great concern to health. Cesium-137, Iodine-131, and Strontium-90. The reason for each is mid-length half life, coupled with strong bio-uptake. Click here for a brief description of each, and why they are so dangerous. TL;DR - they are radioactive, and have a long Biological Half-Life.
Back in the day, there was a super-cool poster called the "Chart of the Nuclides" that you could learn all kinds of interesting stuff from. Below is a snippet of such a chart.
The chart of the nuclides covers every known isotope, with as much data as possible printed into each color-coded little block: Half-life, major and minor decay modes, decay energy, spin, parity, and (sometimes) atomic mass. You can still purchase these wicked cool "Big Bang Theory" props here.
Nowadays, all of that information, and much, much more, is freely available online, by clicking here. There's now also a nifty cellphone app, courtesy of the IAEA (International Atomic Energy Agency).
Lastly I would point to a couple of great articles in Wikipedia. One on Radioactive Decay, and one on Half-Life. If that's too awful and boring to read, you can always play Half-Life on Steam
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