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Why Do Scientists Measure Things by Half-Life?

?Reader @Procrustes tweeted at us to ask: “Why do scientists measure things like radioactive elements in half-life? Why not just measure the whole life?”

If you’re not familiar with the term “half-life,” maybe you’ve heard one of your nerd friends use it. If they weren’t complaining about a guy named Gabe and ranting about steam and a valve, they were probably using it in reference to radiometric dating, a technique that uses measurement of radioactive decay to figure out the age of archaeological artifacts and dinosaur fossils.

Decay and Dating

At the center of every atom is a dense region called a nucleus, which consists of protons and neutrons. In some atoms, the forces in the nucleus are balanced and the nucleus is stable. In others, the forces are unbalanced and the nucleus has an excess of internal energy; it’s unstable, or radioactive. These unstable atoms essentially self-destruct because of the imbalance and break down, or decay. When they do this, they lose energy by emitting energetic subatomic particles (radiation).

These particles can be detected, typically with a Geiger counter. In the case of radiocarbon dating, a common dating method for organic matter that uses carbon-14 (an isotope, or variant, of the element carbon) to estimate age, one radioactive “beta particle” is produced for every carbon-14 atom that decays. By comparing the normal abundance of carbon-14 in a living creature (which is the same concentration in the atmosphere) with the amount left in the material being dated, based on the known decay rate, scientists can figure out roughly how long ago whatever they’re looking at was still alive.

Half-life steps onto the scene in the decay process. While the lifespan of any individual atom is random and unpredictable, the probability of decay is constant. You can’t predict when an unstable atom will break down, but if you have a group of them, you can predict how long it will take. Atoms that have an equal probability of decaying will do so at an exponential rate. That is, the rate of decay will slow in proportion to the amount of radioactive material you have.

“Many will disappear early on in the process but some will last for much longer time periods,” says Dr. Michael Dee, a researcher at Oxford University’s radiocarbon lab. “It’s a bit like putting (a lot) of coins out in the rain. Although they all have an equal probability of being hit by raindrops, many will be struck immediately and others will remain dry, perhaps for an extended period of time.”

It’s easy misinterpret half-life to mean “one half of the time it takes for whatever atoms you’re looking at to decay,” but it actually means “the length of time it takes for one half of the atoms you’re looking at to decay.” The measurement is useful in radiometric dating, says Dee, because exponential decay means “it doesn’t matter how much radioactive material you have, the time taken until half of it is gone [the half-life] is always the same.”

The whole life of the material, on the other hand, would be equal to the lifespan of the last atom in the group to decay. Since an atom’s lifespan is random, inestimable and essentially infinite, the whole life would be, too. It winds up being a not-very-useful measurement. “It’s a bit like one coin sitting out in the rain,” says Dee. “And never getting hit, ever.”

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Big Questions
What is Duck Sauce?
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A plate of Chinese takeout with egg rolls and duck sauce
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We know that our favorite Chinese takeout is not really authentically Chinese, but more of an Americanized series of menu options very loosely derived from overseas inspiration. (Chinese citizens probably wouldn’t recognize chop suey or orange-glazed chicken, and fortune cookies are of Japanese origin.) It would also be unusual for "real" Chinese meals to be accompanied by a generous amount of sauce packets.

Here in the U.S., these condiments are a staple of Chinese takeout. But one in particular—“duck sauce”—doesn’t really offer a lot of information about itself. What exactly is it that we’re pouring over our egg rolls?

Smithsonian.com conducted a sauce-related investigation and made an interesting discovery, particularly if you’re not prone to sampling Chinese takeout when traveling cross-country. On the East Coast, duck sauce is similar to sweet-and-sour sauce, only fruitier; in New England, it’s brown, chunky, and served on tables; and on the West Coast, it’s almost unheard of.

While the name can describe different sauces, associating it with duck probably stems from the fact that the popular Chinese dish Peking duck is typically served with a soybean-based sauce. When dishes began to be imported to the States, the Americanization of the food involved creating a sweeter alternative using apricots that was dubbed duck sauce. (In New England, using applesauce and molasses was more common.)

But why isn’t it easily found on the West Coast? Many sauce companies are based in New York and were in operation after Chinese food had already gained a foothold in California. Attempts to expand didn’t go well, and so Chinese food aficionados will experience slightly different tastes depending on their geography. But regardless of where they are, or whether they're using the condiment as a dipping sauce for their egg rolls or a dressing for their duck, diners can rest assured that no ducks were harmed in the making of their duck sauce.

Have you got a Big Question you'd like us to answer? If so, let us know by emailing us at bigquestions@mentalfloss.com.

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Big Questions
Can You Really Go Blind Staring at a Solar Eclipse?
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A total solar eclipse will cut a path of totality across the United States on August 21, and eclipse mania is gripping the country. Should the wide-eyed and unprotected hazard a peek at this rare phenomenon?

NASA doesn't advise it. The truth is, a quick glance at a solar eclipse won't leave you blind. But you're not doing your peepers any favors. As NASA explains, even when 99 percent of the sun's surface is covered, the 1 percent that sneaks out around the edges is enough to damage the rod and cone cells in your retinas. As this light and radiation flood into the eye, the retina becomes trapped in a sort of solar cooker that scorches its tissue. And because your retinas don't have any pain receptors, your eyes have no way of warning you to stop.

The good news for astronomy enthusiasts is that there are ways to safely view a solar eclipse. A pair of NASA-approved eclipse glasses will block the retina-frying rays, but sunglasses or any other kind of smoked lenses cannot. (The editors at MrEclipse.com, an eclipse watchers' fan site, put shades in the "eye suicide" category.) NASA also suggests watching the eclipse indirectly through a pinhole projector, or through binoculars or a telescope fitted with special solar filters.

While it's safe to take a quick, unfiltered peek at the sun in the brief totality of a total solar eclipse, doing so during the partial phases—when the Moon is not completely covering the Sun—is much riskier.

WOULDN'T IT BE EASIER TO JUST TELL YOUR KIDS THEY WILL GO BLIND?

NASA's website tackled this question. Their short answer: that could ruin their lives.

"A student who heeds warnings from teachers and other authorities not to view the eclipse because of the danger to vision, and learns later that other students did see it safely, may feel cheated out of the experience. Having now learned that the authority figure was wrong on one occasion, how is this student going to react when other health-related advice about drugs, alcohol, AIDS, or smoking is given[?]"

This story was originally published in 2012.

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