Excuse me, do you half the time?

A friend and I were recently talking about Half-life. No, not that Half-life. Half-life as in the time it takes a radioactive isotope to lose (through decay) half of its atoms. So what does that mean and why should you care?

Let’s look at a few key terms first. Remember that big grid on the wall in your high school chemistry class? The one with all the initials in it? That was the Period Table of Elements. I’m sure you know several without even realizing it: Oxygen, Gold, Silver, Tin, Aluminum (and whether you call it tin foil, or aluminum foil nowadays it is always aluminum) Neon, and Calcium to name a few. That’s great you say, but really what’s an element? Well to answer that, let’s look at what makes up an element.

If you zoomed in on an element, all the way down to the atomic level, you would see the atoms that make up that element. An atom is the smallest particle there is that can still be considered of a particular element. You can break an atom into even smaller parts, but what you would be left with would no longer be considered an element.

For example, suppose you decide to throw a birthday party for yourself. You invite a bunch of your friends and even go through the trouble of baking your own birthday cake. After your friends have sung to you, and the candles are blown out, you take the cake and cut it into 20 pieces (one for each of the 20 friends who showed up for your party). Each of your friends can say that they had cake at your party because even though it was just a slice of the whole cake, the slice is still considered cake. Now suppose each of your friends brought a guest to your party (without asking of course) so you were unprepared. In desperation, you cut each of the 20 pieces in half, so now you have 40 pieces to give out. The slices may be smaller and your friends may grumble (that’s what they get for not filling out the RSVP properly) but again, everyone can still say that they had cake. Well suppose some of these so-called friends of yours brought kids without telling you (are you kidding me???). Now you try to break some of the slices down even further. In fact, you break them down so far that they are back into their original ingredients: flour, butter, sugar, eggs, vanilla, baking powder and the secret ingredient, love. As much as your friends might enjoy eating a pile of baking powder, they can no longer claim that they’ve had a piece of cake. The cake was broken down so far that it could no longer be considered cake anymore. Sucks to be them.

An atom is like a slice of an element. It’s still a piece of the whole and can still be called cake (or oxygen or helium or what have you). However if you broke that atom down any further, into its electrons, protons and neutrons, you could no longer call it an atom of oxygen or helium. Just like the egg itself can’t be called cake, its just an ingredient.

So now we know what an atom is and I’ve also inadvertently mentioned the 3 components of an atom: electrons, protons and neutrons. Atoms of different elements have different combinations of these three particles. The number of protons and electrons in an atom are always equal. For example, the element Hydrogen has 1 proton and 1 electron in its atoms. It’s atomic number is said to be 1. This puts it in position number 1 on the Periodic Table. What would happen if that atom had 6 protons and 6 electrons? Well then it would no longer be Hydrogen, it would be Carbon. Carbon’s atomic number is 6 and that puts it in position number 6 on the Periodic Table. This pattern is the same for all of the elements.

But what about the neutrons you say? Well I was saving the best for last. Neutrons are located in the nucleus (center) of the atom along with the protons. The electrons “orbit” around the nucleus. The number of protons in an atom plus the number of neutrons equals the atomic mass of the atom (that’s not the same as the atomic number). While the number of protons in an atom are always the same, the number of neutrons can vary. Atoms of the same element that have different amounts of neutrons are called isotopes. An isotope of carbon (number 6 on the Periodic Table) might have 12, 13 (which is rare) or even 14 neutrons. Therefore Carbon-12, Carbon-13 and Carbon-14 are all said to be isotopes of Carbon. All 3 isotopes still have 6 protons and 6 electrons as we said before, otherwise they couldn’t be called carbon.

Now back to Half-life (Seriously? You’re not not done yet??? Stick with it, we’re almost there!)

Not all of these isotopes are stable. When an isotope is unstable it is said to be radioactive and can go through a spontaneous decay. There are several different ways that an isotope can decay, but I’ll only mention two of the more common types. The first type of decay is when a proton in the atom turns into a neutron. When this happens, the atomic mass doesn’t change (because we said protons + neutrons = mass). So think 19 protons + 21 electrons = atomic mass 40 or 18 protons + 22 neutrons = atomic mass 40. Either way it’s 40.

The second type of decay is the opposite, when a neutron in the atom turns into a proton. Again, when this happens, the atomic mass doesn’t change (because we said protons + neutrons = mass). So think 6 protons + 8 neutrons = atomic mass 14 or 7 protons + 7 neutrons = atomic mass 14. Either way it’s 14.

The important change here is the number of protons. Remember, the number of protons defines what element the atom makes up. So in our first example of decay, even though the mass number stayed at 40, the number of protons went from 19 down to 18. If we look at the Periodic Table we see that Potassium is number 19 and Argon is number 18. So when the isotope Potassium-40 decays, it becomes Argon-40. In the second example of decay, we went from 6 protons to 7. Since Carbon is number 6 on the Periodic Table and Nitrogen is number 7 we can see that Carbon-14 decays into Nitrogen-14.

All isotopes of a particular element decay at a certain, exponential rate. This rate is fixed for that particular isotope and is called the half-life, or the number of years it would take for half of the atoms to decay. Potassium-40’s half-life is (and always is) 1,260,000,000 years (1.26 billion). The half-life of Carbon-14 is 5,730 years.

All living things (or things that were once living) have carbon in them. Plants take in carbon from the air and convert it into sugars. Animals (including people) eat plants, or indirectly eat other animals who ate the plants. Carbon therefore makes its way into all living things. Remember we said that there were 3 types of carbon, although Carbon-13 is so rare that we don’t need to consider it. So the carbon in your body is either Carbon-12 (stable) or Carbon-14 (unstable). The ratio of Carbon-12 to Carbon-14 in your body is approximately the same as it is in my body, my friend’s body, a whale’s body, or a tree’s “body” (all living things). Don’t be too concerned though, it’s the same ratio that is found in the atmosphere. This ratio does not change much through history (although it’s change can be checked for accuracy in trees, and that’s a whole other post).

So knowing this ratio, we are able to take something that was deceased (cut off from the intake of carbon) and check it’s ratio of carbon-12 (stable) to carbon-14 (unstable) compared with something that is alive. Knowing that the half-life of carbon-14 is 5,730 years, we can date the deceased object by the amount of carbon-14 that has decayed. That’s the power of half-life!

FYI: This same dating technique can be done with Potassium-40 (which I mentioned above), but Potassium-40 is found in rock, not in living things.


About additionaddiction

My thoughts on life, atheism, science, and the human race

Posted on September 28, 2011, in Biology, Chemistry, Mathematics, Physics, Time and tagged , , , , , , , , , , . Bookmark the permalink. Leave a comment.

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