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.”
The popularity of bird-watching, camping, and hiking has skyrocketed this year. Whether your gift recipients are weekend warriors or seasoned dirtbags, they'll appreciate these tools and gear for getting most out of their hiking experience.
1. Stanley Nesting Two-Cup Cookset; $14
Stanley’s compact and lightweight cookset includes a 20-ounce stainless steel pot with a locking handle, a vented lid, and two insulated 10-ounce tumblers. It’s the perfect size for brewing hot coffee, rehydrating soup, or boiling water while out on the trail with a buddy. And as some hardcore backpackers note in their Amazon reviews, your favorite hiker can take the tumblers out and stuff the pot with a camp stove, matches, and other necessities to make good use of space in their pack.
2. Osprey Sirrus and Stratos 24-Liter Hiking Packs; $140
Osprey’s packs are designed with trail-tested details to maximize comfort and ease of use. The Sirrus pack (pictured) is sized for women, while the Stratos fits men’s proportions. Both include an internal sleeve for a hydration reservoir, exterior mesh and hipbelt pockets, an attachment for carrying trekking poles, and a built-in rain cover.
Nothing beats ice-cold water after a summer hike or a sip of hot tea during a winter walk. The Yeti Rambler can serve up both: Beverages can stay hot or cold for hours thanks to its insulated construction, and its steel body (in a variety of colors) is basically indestructible. It will add weight to your hiker's pack, though—for a lighter-weight, non-insulated option, the tried-and-true Camelbak Chute water bottle is incredibly sturdy and leakproof.
4. Mappinners Greatest 100 Hikes of the National Parks Scratch-Off Poster; $30
The perfect gift for park baggers in your life (or yourself), this 16-inch-by-20-inch poster features epic hikes like Angel’s Landing in Zion National Park and Half Dome in Yosemite National Park. Once the hike is complete, you can scratch off the gold foil to reveal an illustration of the park.
5. National Geographic Adventure Edition Road Atlas; $19
Hikers can use this brand-new, updated road atlas to plan their next adventure. In addition to comprehensive maps of all 50 states, Puerto Rico, Canada, and Mexico, they'll get National Geographic’s top 100 outdoor destinations, useful details about the most popular national parks, and points on the maps noting off-the-beaten-path places to explore.
6. Adventure Medical Kits Hiker First-Aid Kit; $25
This handy 67-piece kit is stuffed with all the things you hope your hiker will never need in the wilderness. Not only does it contain supplies for pain, cuts and scrapes, burns, and blisters (every hiker’s nemesis!), the items are organized clearly in the bag to make it easy to find tweezers or an alcohol wipe in an emergency.
Trekking poles will help increase your hiker's balance and stability and reduce strain on their lower body by distributing it to their arms and shoulders. This pair is made of carbon fiber, a super-strong and lightweight material. From the sweat-absorbing cork handles to the selection of pole tips for different terrain, these poles answer every need on the trail.
What can’t this multitool do? This gadget contains 19 hiking-friendly tools in a 4.5-inch package, including pliers, screwdrivers, bottle opener, saw, knife, hammer, wire cutter, and even an emergency whistle.
Don’t let your hiker get caught off the grid with a dead phone. They can charge RAVPower’s compact power bank before they head out on the trail, and then use it to quickly juice up a phone or tablet when the batteries get low. Its 3-inch-by-5-inch profile won’t take up much room in a pack or purse.
Neither rain, nor snow, nor hail will be a match for these waterproof, tearproof 3.5-inch-by-5.5-inch notebooks. Your hiker can stick one in their pocket along with a regular pen or pencil to record details of their hike or brainstorm their next viral Tweet.
In 1947, Congress proposed the 22nd Amendment, which would officially limit each U.S. president to two four-year terms. But while the two-term maximum was new, the length of each term wasn’t—presidents had been serving for four years at a time ever since George Washington’s tenure.
Why Are Presidential Terms Four Years Long?
In May 1787, representatives from every state except Rhode Island gathered in Philadelphia for the Constitutional Convention, where they planned to update the Articles of Confederation and give more power to the practically impotent federal government. What they ended up doing was drafting a new document—the Constitution—and basically overhauling the entire political system. Chief among the changes was the creation of an executive branch to provide checks and balances for the legislative and judicial branches.
Since the delegates were wary of ending up with a monarch-like ruler, there was a lively debate over how long the president should be allowed to serve. Some, like North Carolina’s Hugh Williamson, supported a single seven-year term, with no opportunity for reelection. That way, he argued, they could avoid an “elective king,” who would “spare no pains to keep himself in for life, and … lay a train for the succession of his children.” If a president could only serve one term, Williamson wasn’t against a 10- or even 12-year term. His colleagues proposed other lengths, from a modest six years all the way to “for life.” Alexander Hamilton was among those who advocated for a lifelong term, thinking it would prevent the president from being too focused on reelection to make good decisions.
They were having just as much trouble deciding whether Congress or the general population should choose the president. These discussions dragged on through the summer, until the delegates appointed an 11-member “Committee on Postponed Matters” to come up with a final solution [PDF]. Under the committee’s plan, the president would be elected by an electoral college—a clear compromise between letting Congress pick someone and leaving it entirely up to the voters. The president would serve for four years, and could run for reelection. In early September, the exhausted delegates approved the plan. (North Carolina was the only state to vote against the four-year term.)
Why Can a President Only Serve Two Terms?
Though the Constitutional Convention had agreed not to set term limits for the president, George Washington and Thomas Jefferson established a precedent by bowing out after just two. Most future presidents followed suit, and the ones who didn’t failed to win a third term anyway. Ulysses S. Grant, for example, had taken a break after his second term ended in 1877, and campaigned for a third one in 1880. He nearly won the nomination at that year's Republican National Convention, but lost it to James Garfield. Theodore Roosevelt also declined to seek a third term after his two were over, only to change his mind a few years later. He ran as a third-party candidate for his newly established Progressive Party in 1912, but Democrat Woodrow Wilson came out on top.
Things changed in the 1940s, when Democrat Franklin Delano Roosevelt clinched his third, and then fourth, presidential victory. Between the fallout from the Great Depression and U.S. involvement in World War II, it was an especially turbulent era for the nation, which likely influenced voters to favor consistency over someone new. That said, some people (Republicans in particular) were uncomfortable with such a long reign. Thomas Dewey, who ran against Roosevelt in 1944, called it “the most dangerous threat to our freedom ever proposed.”
Roosevelt died in office just months into his fourth term, and members of Congress soon began working on an amendment to prevent the kind of political dynasty that Williamson had been worried about in 1787. They introduced the 22nd Amendment in March 1947, and it was ratified in February 1951.
Can a President Serve More Than Eight Years?
There is a way for the president to spend a couple of extra years in the Oval Office. The 22nd Amendment states that no person who has been president “for more than two years of a term to which some other person was elected President shall be elected to the office of President more than once.” In other words, if a vice president (or another person in the line of succession) ends up serving out less than two years of a term for someone who resigned, died, or was impeached, they can technically serve for two terms of their own. In that case, they will have spent 10 years as POTUS.
Why Does the President Have Term Limits, But Congress Doesn’t?
While term limits for Congress did get discussed during the Constitutional Convention, the delegates ultimately decided not to set those boundaries on the legislative branch. As James Madison explained in The Federalist Papers (No. 53), some Founding Fathers thought there were advantages to long-sitting senators and representatives.
“A few of the members, as happens in all such assemblies, will possess superior talents; will, by frequent reelections, become members of long standing; will be thoroughly masters of the public business, and perhaps not unwilling to avail themselves of those advantages,” he wrote. “The greater the proportion of new members, and the less the information of the bulk of the members the more apt will they be to fall into the snares that may be laid for them.”
In other words, he predicted that career politicians would become experts, while high turnover rates would lead to confusion and corruption. While many people disagree with this line of thinking today, the fact that congressional term limits weren’t originally included in the constitution has made it difficult to enact them now. Some states have tried to do it in the past, but the Supreme Court ruled them unconstitutional in 1995 (in a 5-4 vote). To reinstate them, we’d need to pass a whole new amendment.
How Can You Change Presidential Term Limits?
Since repealing an old amendment doesn’t have its own process, altering the two-term limit (or the four-year term length) would also require a new amendment. For a proposed amendment to get passed, two-thirds of both the Senate and the House of Representatives must vote in favor of it. After that, at least three-fourths of the states must ratify it.
There is one other way to pass a new amendment, but it’s never been done before. If two-thirds of state legislatures agree to call for another constitutional convention, they could draft their own amendment without congressional approval. (They would, however, still need 38 of 50 states to ratify it.)
Though the president may sign amendment certifications as a witness, the gesture is entirely ceremonial. The White House has no authority over or involvement in the amendment process—not even by executive order.