Subject: Can someone please explain?
Posted by: Mixamatosis
Date: Jan 21 17
I've read that it's dangerous to mix ammonia and bleach. Variously I've read that it can produce deadly cyanide gas, chlorine gas (which is said to be bad for you) and even explosions.
However swimming pools are kept fit for use with chlorine, and our urine contains ammonia but then we may clean toilets with bleach. Also many cleaning products contain either ammonia or bleach and it would be easy to use them unthinkingly in combination.
How is it that people aren't generally harmed by these dangers when swimming in swimming pools or doing daily cleaning, or are we being harmed at low level and is the harm cumulative?
Posted by: Mixamatosis
Date: Jan 21 17
I've read that it's dangerous to mix ammonia and bleach. Variously I've read that it can produce deadly cyanide gas, chlorine gas (which is said to be bad for you) and even explosions.
However swimming pools are kept fit for use with chlorine, and our urine contains ammonia but then we may clean toilets with bleach. Also many cleaning products contain either ammonia or bleach and it would be easy to use them unthinkingly in combination.
How is it that people aren't generally harmed by these dangers when swimming in swimming pools or doing daily cleaning, or are we being harmed at low level and is the harm cumulative?
526 replies. On page 24 of 27 pages. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
Catreona 
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Apologies, Brian, if you have touched on this - I've only read the first three pages of the thread. Not knowing this thread was here, a few weeks ago I posed a science question to my non FT blog community, which includes a science writer and a chemist cum toxicologist. Wanted to post it now before I forgot, for anyone who might be interested. Q: Here's what is probably a really dumb question, but it's been niggling at the back of my mind for some time. The definition of 'year' is the time it takes Tellus to complete one revolution about Sol, right? So then how is it possible to speak, say, of so many thousand or million years after the Big Bang, in a context that can, by its very nature, have no reference to the Sun, much less to the Earth? A: I believe the year is officially defined as so many oscillations of the atomic clock. IIRC, it is periodically adjusted to keep it in tune with the Earth's period of revolution about the sun. That's a few seconds at most, though. So the length of the year is fixed for all practical purposes and you can extend that measure of time as far back or forward as you wish. Reply #461. Feb 19 20, 3:07 PM |
brm50diboll
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I agree with the answer you were given above. Time was originally defined in human history by astronomical cycles. But in our modern concept of time, it is determined by something which can be measured extremely accurately in a lab designed for that purpose. So the time period "year" existed before the sun existed. (Of course there were no people around either in that cosmological era.) As a matter of strict fact, the amount of time for the Earth to complete one revolution around the Sun actually *slowly changes* over the eons. A solar year today is slightly different from a solar year during the Mesozoic Era (age of Dinosaurs) due to alterations in Earth's orbit and changes in angular momentum from gravitational interactions with other bodies in the solar system. But our modern definition of "year" means the year as it currently exists, even though the astronomical solar year changes somewhat. To further complicate the matter, there are slight differences in the solar year, sidereal year, and other definitions of the year (such as the time between two perihelions of the Earth in its orbit around the Sun) that I would rather not get into. All of these various different types of "years" differ only slightly, so 13.8 billion years is still a good estimate even if we were picky about which type of astronomical year we were referring to. Reply #462. Feb 19 20, 4:23 PM |
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Attempts to determine Hubble's Constant, which measures the rate of expansion of the universe, have been complicated by conflicting data. This remains an area of intense active research. We do know that very early on after the Big Bang there was a brief period of "inflation" when the universe was expanding much faster than it is now, followed by a slower rate, and current data suggests that the rate of expansion is beginning to increase again (though slightly), which suggests the theory that there will someday be a "Big Crunch" where the universe stops expanding and begins to contact again isn't going to happen. The apparent reason for this is "dark energy". Worthy of a long post all to itself. Reply #463. Feb 23 20, 10:42 PM |
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Begins to contract again, not contact. I hate typos. Reply #464. Feb 23 20, 10:43 PM |
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What is called "Dark Energy", Einstein called the cosmological constant. In his equations for general relativity (which I admit I do not understand, although I do understand his equations for special relativity), he recognized that the original equation predicted the universe would expand over time. To remedy this (as Hubble's data indicating the expansion of the universe had not happened yet), Einstein introduced into his equation a "fudge factor" he called the cosmological constant to keep the universe's size constant. When later he saw Hubble's data indicated the universe was indeed expanding, he called his cosmological constant "the greatest mistake of my life". On a side note, scientists frequently introduce "fudge factors" into equations to get results that are consistent with experimental data. Sometimes this indicates a fundamental flaw in the theory itself, and other times it turns out to be something that can be explained and accurately quantified as the theory matures. In any event, Einstein's renunciation of his cosmological constant appears to have been premature. Apparently, there is something in the very fabric of space itself that causes it to expand. If unopposed by gravity, this expansion would accelerate out of control, leading eventually to what theoretical physicists have termed the "Big Rip". This factor is now called dark energy. More on this later. Reply #465. Mar 07 20, 8:29 PM |
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But first: The so-called "singularity" may be imaginary. No one knows what's inside a black hole. If you find someone who does think they know what's inside a black hole, ask them *privately* to explain it to you and see if you can follow it, then privately ask a trusted friend or family member to read it and see if it makes any sense to them. Mine certainly wouldn't, so I'm not going to try. I'm just an amateur. I do love astronomy. Reply #466. Mar 21 20, 11:33 AM |
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The idea behind dark energy is that it is the reason space expands. This effect is not noticeable anywhere there is appreciable gravity around (such as inside our Milky Way Galaxy), but in the deep voids of intergalactic space, far from significant collections of matter, gravity is sufficiently weak for the expansion of space over time to occur. This expansion was particularly marked in the early period after the Big Bang known as the Inflationary Era. In fact, it led to a bit of apparent paradox. That is, for a brief time during the Inflationary Era, the Universe was expanding faster than the speed of light. Isn't it impossible for anything to go faster than the speed of light? For matter, yes. Even for photons (massless particles of light), again, yes. But for space itself, it turns out no, because empty space is *nothing* and while particles cannot exceed the speed of light in a vacuum, c, *nothing* can expand faster than light speed. What this means is that there are parts of our original universe now that are now forever outside our ability to reach because of Inflation. As the density of dark energy fell in the Inflationary Era, gravity reasserted itself and Inflation stopped, leading to a very long period of relatively stable expansion of the Universe at a much reduced rate. Recent calculations seem to indicate the rate of expansion is very slowly beginning to trend upward again. Why? Because gravity keeps weakening as the density of matter in the universe falls in the expanding Universe. Early speculation was that the Universe might someday stop expanding and then begin to contract, leading to an eventual "Big Crunch". Current data suggest that won't happen and the Universe will expand forever, eventually at an accelerating rate that will tear apart atoms called "The Big Rip". But the time period for that to happen is so huge (well beyond trillions of years, so huge it can only be expressed in scientific notation, like 10^35 years or some such.) By that time, all stars will have burnt out and the Universe will be a cold, dead place. At this point, current theory of the future of cosmology reads more like science fiction than it does of physics. That is actually a problem for physics, as theories which are not testable aren't useful. Reply #467. Jun 12 20, 1:37 PM |
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I wanted to depart astronomy for awhile and discuss physics. This isn't too much of a departure, as astronomy is actually a branch of physics. But I am switching from examining the very large to examining the very small. In grade school, we are taught that matter is composed of atoms and that atoms contain protons, neutrons, and electrons. The protons and neutrons are found in the very tiny atomic nucleus, where they make up over 99.9% of the mass of the atom, despite the fact the nucleus is much smaller than even the atom itself. The electrons, which are extremely lightweight, move around the nucleus. Protons are positively charged, neutrons are neutral, and electrons are negatively charged. If the atom is overall neutral, the number of protons equals the number of electrons. If there is an imbalance between the number of protons and electrons, the atom has a net charge and is known as an ion. We are told that electrons are kept in place in the atom by the electric force, where like charges repel and opposite charges attract. Since protons and electrons have opposite charges, they are attracted to each other, but since electrons are vastly lighter than protons, the electrons do the moving in the atom and the protons are relatively stationary ("flies buzzing around an elephant" is one description of the electron's relationship to the protons). So far, so good. Basic elementary school description of the atom. But the actual atom is vastly more complex than this, and to begin to understand why, we can start with questions: If like charges repel and opposite charges attract, then why aren't the electrons "sucked into" the nucleus? Also, how does the nucleus hold together if protons which are all positively charged repel each other? Surely the neutrons aren't holding the protons together through the electric force, as they are neutral, so the nucleus has a net positive charge. If the electric force was the only force involved here, the only atoms that should exist would be hydrogen, since once you have more than one proton in the nucleus, the repelling electric force should blow the nucleus apart. Well, to understand the answers to those questions we must accept that there are several forces in nature. The current "Standard Model" describes four fundamental forces in nature: 1) Gravity 2) The Electromagnetic force 3) The Strong Nuclear Force and 4) The Weak Nuclear Force. More on the properties of those four fundamental forces, especially the last two, next time. Reply #468. Jul 02 20, 8:48 PM |
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OK. The force of gravity is most different from all the other forces and is weakest, by far. But it shapes the structure of our universe, which is built of very massive objects where gravity can manifest itself. Electromagnetism - the electric force and the magnetic force are related but not the same. The relationship is complex and governed by Maxwell's equations - the summit of 19th century physics. Both electricity and magnetism, like gravity, follow inverse square laws, which state the forces weaken as to the inverse of the square of the distance between the interacting bodies. Electromagnetism is much stronger than gravity, but has no effect on neutral particles. Unlike gravity, which is always attractive and never repulsive, electromagnetism can be either attractive or repulsive, depending on the particles involved in the interaction. The strong nuclear force - this force is the strongest of the four fundamental forces and is what holds the nucleus together. It does not follow an inverse square law. At distances comparable or smaller than the size of a nucleus (about one picometer (10^-12 meter)) the SNF overpowers the electric force and holds the nucleus together. But outside the tiny nuclear distances, the SNF is virtually nonexistent and protons will repel each other unless forced extremely closely together. At an even more fundamental level, the SNF is responsible for binding the quarks together inside hadrons like protons and neutrons. The actions of the SNF are described by an advanced area of physics called quantum chromodynamics. The weak nuclear force governs certain types of radioactivity. The WNF is stronger than gravity but weaker than electromagnetism. Like the SNF, the WNF does not follow an inverse square law and is therefore only significant at extremely tiny distances. An example of the WNF at work: inside a nucleus that is stable, such as carbon-12, the neutrons are stable. But a *free* neutron, one outside a nucleus, is radioactive and will break down with about a 12 minute half-life into a proton, an electron, and an electron antineutrino by the actions of the WNF. Each of the four fundamental forces has particles which "carry" that force. More on that later. Reply #469. Aug 02 20, 6:26 PM |
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So the first "carrier" particle of forces to be discovered was the photon, the carrier of the electromagnetic force. It has a number of interesting properties. The name photon comes from the Greek word for light, as visible light is composed of photons with wavelengths between 400 nm (nanometers or one-billionth of a meter) and 700 nm, approximately. Photons always travel at the speed of light (which, in a vacuum is c, approximately 300 million meters per second) and have no charge and no rest mass. Photons have unlimited range, a consequence of their zero rest mass. Photons are their own antiparticle, which is very unusual among the members of the particle "zoo". Photons have both wavelength and frequency, which are inversely related to each other. In other words, as the wavelength increases, the frequency decreases and vice versa. Photons with wavelengths outside the 400-700 nm range are not visible forms of radiation, but other types, known as the electromagnetic spectrum. Included in that are radio waves, microwaves, infrared light, visible light, ultraviolet light, X-rays, and gamma rays. (I put them in order from lowest energy to highest energy.) There are other forms of radiation not on the electromagnetic spectrum, but those other forms are carried by other particles, not photons. When other particles meet their corresponding antiparticles, both are annihilated and photons are produced, typically gamma ray photons of extremely high energies. Reply #470. Sep 02 20, 5:14 PM |
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A little random science thought before I resume my discussion of subatomic physics: https://tinyurl.com/yxtbpwsjReply #471. Sep 09 20, 11:48 AM |
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The carrier particle for the gravitational force is said to be the graviton. I stated it as "said to be" because the particle has not been actually verified to exist, and current theory suggests a graviton detector cannot actually be constructed because of the extremely weak interactions of this particle with matter. What is needed is a working theory of quantum gravity, which does not presently exist. Current quantum theory (the so-called "standard model") is able to incorporate the other three fundamental forces, but not gravity, and the mathematics of general relativity (which does describe gravity), seems incompatible with the mathematics of quantum theory. Although the graviton itself seems undetectable with our present understanding of physics, there has been a effort to design construction of gravity wave detectors. Gravity waves are believed to occur when extremely massive objects interact, such as the collision of two neutron stars or two black holes. Such events would be extremely rare, but given the sheer size of the universe, they probably do occur in some distant parts of the universe from time to time, and perhaps the gravity waves they would generate could be detected. Reply #472. Oct 06 20, 10:28 AM |
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The carrier particle of the strong nuclear force is called the gluon. The gluon has mass, which limits its range. Consequently, it is effective only over very tiny distances, on the order of one picometer (10^-12 meter, a trillionth of a meter), which is a distance found in atomic nuclei, but not in whole atoms. What this means is that the SNF only works at distances comparable to the size of atomic nuclei. For distances beyond this, the SNF is essentially non-existent. In the historical development of subatomic theory, it was originally thought that the carrier of the SNF was a type of subatomic particle called the pion (or pi meson), and that the SNF was carried out by exchanges of pions between the protons and neutrons of atomic nuclei. But the development of quark theory lead to the realization that mesons and baryons are themselves composed of even smaller particles called quarks, which possess fractional charges. A proton, for example, is composed of two up quarks and a down quark, whereas a neutron is composed of two down quarks and an up quark. Mesons like pions are composed of quark-antiquark pairs. The development of quark theory led to the realization that the *true* carrier of the SNF was not a particle that bound the protons and neutrons together in a nucleus, but actually it was a particle that bound quarks together inside hadrons (which include protons, neutrons, and mesons, but *not*, importantly, electrons, which are an entirely different type of particle known as a lepton which does not "feel" the SNF, which is why electrons are not in the nucleus.) This true carrier of the SNF is the gluon, so-called because it "glues" quarks together so tightly that isolated single quarks are not seen in matter under normal conditions. In effect, the binding of protons and neutrons in a nucleus is a "side effect" of the binding of quarks in hadrons. The properties of the SNF is described quantitatively in s branch of the so-called "Standard Model" of quantum theory known as quantum chromodynamics. See how simple subatomic physics is? Reply #473. Nov 03 20, 9:22 PM |
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Another interlude before I return to my discussion of subatomic physics: https://tinyurl.com/y2zpwqvz Yes. That is indeed none other than Weird Al Yankovic himself as Sir Isaac Newton. Reply #474. Nov 09 20, 4:47 PM |
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The carriers of the weak nuclear force are the W+, W-, and Z bosons. Of the four fundamental forces, the weak nuclear force is the most difficult to explain. Some background in subatomic particle properties is needed. For example, understanding what a boson is and how it different from a fermion. Knowing the main types of fermions: hadrons and leptons, and the difference between the two. Knowing the main types of hadrons: mesons and baryons, and knowing the difference between these two. In short, we need a primer on: The Particle Zoo In elementary school, kids are taught that atoms are composed of protons, neutrons, and electrons. But there are actually hundreds of subatomic particles. The vast majority of these particles are unfamiliar because they are extremely unstable and decay into other subatomic particles in extremely short periods of time, less than 10^(-8) seconds in most cases. At the time that they were being discovered in the 1930s to 1950s (for the most part), they were very confusing because they seemed to have no clear pattern in their charges, masses, and other properties. So they got called the Particle Zoo. Attempts to discover order in the Particle Zoo, to develop a classification scheme for them (analogous to classification of living organisms in biology) lead to the discovery that many of these particles appeared to have internal structure of their own and could be divided into still smaller particles. In the 1960s, order finally began to emerge from the chaos with the development of quark theory. That is where I need to go next before I can adequately address the issue of how the weak nuclear force works. Reply #475. Nov 30 20, 8:49 PM |
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OK. So let's look at a simplified classification scheme for The Particle Zoo. The first division is between the bosons and the fermions. Bosons are named after Satyendra Nath Bose, a famous Indian physicist. They are force-carrying particles like those I've previously mentioned (photons, gravitons, gluons, W+, W-, and Z particles) and possess a whole number value of a quantum property called "spin", which despite the image that is evoked in the mind, has nothing to do with tiny spheres spinning. More importantly, bosons do not obey certain laws associated with the other main branch of particles, the fermions, which means they do not obey the Pauli Exclusion Principle or the Law of Conservation of Fermion number, which means as many of them as you want can be packed anywhere and they can be more easily created and destroyed than the fermions. The fermions, named after the famous Italian physicist Enrico Fermi (who also had Element 100 named after him), have half-integer spin and are bound by the two laws I just mentioned. The familiar protons, neutrons, and electrons are in the fermion group along with many very unfamiliar particles. I'll have more to say about the bosons when I resume my discussion of fundamental forces, but for now, let's look at the fermions, which can be further subdivided into two major groups itself: the hadrons and the leptons. Hadrons are particles that have further internal structure, containing quarks or antiquarks with fractional charges. Leptons do not contain quarks and can not be further subdivided. Protons and neutrons are hadrons and contain quarks. Electrons are leptons and do not contain quarks. An electron is an electron is an electron. Hadrons are subject to the strong nuclear force carried by the gluon boson. Leptons do not "feel" the strong nuclear force. Quarks, which make up hadrons, are divided into six families. There are also antiquarks for each quark with exactly the same mass as the corresponding quark, but with opposite charge. The six families of quarks are grouped into three levels with two families apiece. At level 1 are the up and down quarks. The up quark has a charge of +2/3, and the down quark has a charge of -1/3. For comparison, an antiup quark (which is *not* a down quark) has a charge of -2/3, and an antidown quark (which is *not* an up quark) has a charge of +1/3. A proton contains two up quarks and one down quark for a net charge of +1, and a neutron contains two down quarks and one up quark for a net charge of 0. At level 2, we have the unstable strange and charmed quarks, and, at level 3, we have the extremely unstable bottom and top quarks. All quarks have corresponding antiquarks. Hadrons may be further subdivided into two divisions themselves, the baryons and the mesons. Baryons (meaning "heavy") contain three quarks, one of each of the three primary "colors" (red, green, and blue - green, not yellow - there is no yellow quark - the "colors", like "spin", have nothing to do with real color). Mesons are composed of quark-antiquark pairs. An example would be a meson containing a red up quark and an antired down antiquark. All mesons are unstable and decay into other particles in fractions of a second due to the effect of the weak nuclear force. The leptons, which do not contain quarks, are also divided into six families grouped in pairs at three levels. At level 1, we have the electron and the electron neutrino. Like quarks, leptons also have antiparticles. The antiparticle for the electron, the antielectron, is more commonly called the positron, and has the same mass as an electron but with an opposite +1 charge from an electron. The neutrinos have *almost* zero mass and are all electrically neutral. They do have *some* mass, theories predict, but it has not been accurately measured as of yet. Neutrinos travel at nearly the speed of light and rarely interact with other particles, so they are sometimes called "ghost" particles. At level 2 of the leptons we have the muon and the muon neutrino (and their corresponding antiparticles). The muon has a -1 charge like an electron, but is much more massive and unstable, and it decays into an electron and various neutrinos and antineutrinos by the effect of the weak nuclear force. At level 3 of the leptons we have the tau particle (also with a -1 charge like an electron), a tau neutrino, and their corresponding antiparticles. The tau particles are *extremely* unstable. The three classes of neutrinos (electron neutrino, muon neutrino, and tau neutrino) all have zero charge and very tiny masses which have not been accurately measured, but it is believed that the masses increase with level. There is also an antineutrinos for each neutrino (antineutrinos also have zero charge and tiny masses). Recent experiments have shown that the three classes of neutrinos spontaneously "oscillate"; that is, they can change from one level to a different level unpredictably. See how simple all that was? You now understand the basics of The Particle Zoo. Back to the Weak Nuclear Force next time. Reply #476. Dec 10 20, 2:21 PM |
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Got a good look at the Jupiter-Saturn conjunction tonight. Happy Winter Solstice, everyone! Reply #477. Dec 21 20, 7:19 PM |
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OK. We are now ready to look at how the Weak Nuclear Force operates. A good way to illustrate the process is to use Feynman diagrams (after the great Nobel prize-winning American physicist Richard Feynman), but as this format does not support diagrams, I will describe the process verbally and attach a link which shows the relevant Feynman diagram. There are many processes mediated by the WNF, but the one I will choose for my example is a particularly important one: neutron decay. Many people are under the impression that neutrons are stable particles like protons and electrons. This is actually false. Neutrons inside atomic nuclei are stable (if the nucleus itself happens to be stable) for a variety of reasons, including exchange of quarks between adjacent protons and neutrons, but a *free* neutron (one outside a nucleus), is actually unstable and radioactive with a half life of about 10.3 minutes, decaying into a proton, an electron, and an electron antineutrino. The process of neutron decay is mediated by the WNF. Actually what happens is one of the down quarks in a neutron becomes an up quark, changing the particle to a proton. The other down quark and the up quark in the neutron is unaffected by the decay process. The down quark (charge negative one-third) changes to an up quark (charge positive two-thirds) by releasing a W- boson, (charge negative one), which is a carrier for the WNF. The W- boson then breaks down into an electron and an electron antineutrino, completing the process. Several important conservation laws must be followed in this decay process and, in fact, *are* followed: conservation of mass-energy, conservation of momentum, conservation of charge, conservation of spin, conservation of quark number, and conservation of lepton number. Here is the link with the Feynman diagram for neutron decay: https://tinyurl.com/y68hwbqxThe details are well-illustrated in the video, but I want to focus on a few of the conservation laws here. Conservation of charge is satisfied because a neutron (before) has a charge of 0, and a proton, electron, and electron antineutrino (after) has a net charge also of 0, as the proton has a charge of +1, which is cancelled by the -1 charge of the electron, and the electron antineutrino has a charge of 0. Quark number is 3 for the neutron (two downs and an up, before) and is also 3 for the proton (two ups and a down, after, since the electron and the electron antineutrino both have quark numbers of 0 since neither contains quarks as they are leptons). Lepton number is 0 for the neutron (since a neutron is a hadron, not a lepton) and the net lepton number after is also zero since the proton has a lepton number of 0 (because, like the neutron, it is a hadron, not a lepton), and the electron has a lepton number of +1 (because an electron is a lepton) , but this +1 is cancelled by the -1 lepton number of the electron antineutrino, because an antineutrino is an *antilepton*, so the net lepton number after the decay process remains 0. Many different types of radioactive decay are mediated by the WNF. The grisly details involve solving complicated differential equations, but I think it will be worth it to discuss the topic of half-life next time. Reply #478. Jan 15 21, 7:11 PM |
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But first, another interlude: https://tinyurl.com/y3wtbh62 Ah, the Onion. "Horrifying Planet" was a great "documentary" science series. "Even developed a system of ethics that justifies it." Reply #479. Jan 30 21, 1:45 PM |
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As someone who has taught the concept of half life in both chemistry and physics classes over the years, I believe I have become fairly familiar with the typical misconceptions students have of this. A starting point for this discussion would be to address the most common misconception about half life I encounter. A book definition of half life will say that it is the time required for half of a given radioactive material to decay. Students often believe that if half of a material decays in X amount of time, then during another X amount of time, "the other half" will decay and none of the original material will be left. For some students, it is very difficult to clear up this line of confused thinking. In chemistry, it turns out that radioactive decay is a subset of a more general class of kinetics (the study of *rates* of processes) known as first-order kinetics. The fallacy that I described would actually be true if radioactive decay followed a zero-order kinetic rate law. But it does not. First-order kinetics is actually very common, whereas zero-order kinetics is fairly rare. First-order means that the decay rate is proportional to the concentration of the material. As a material decays, its concentration decreases and so the rate that it decays further also decreases. It turns out "the second half" of the original material never really completely decays to zero because as you have less and less of the material, the slower the remaining material disappears. Consider a hypothetical example of 256 g of a radioactive material with a half life of exactly 1 year: After 1 year from the original measurement of 256 g, half will have decayed and so 128 g will remain. After another year (2 years total from the original measurement), half of the 128 g will have decayed and 64 g will remain. After another year (3 years total from the original measurement), half of the 64 g will have decayed and 32 g will remain. Continuing this pattern, we see: 16 g will remain after 4 years 8 g will remain after 5 years 4 g will remain after 6 years 2 g will remain after 7 years 1 g will remain after 8 years 0.5 g will remain after 9 years 0.25 g will remain after 10 years 0.125 g will remain after 11 years 0.0625 g will remain after 12 years.... Note that the number approaches zero *in the limit* (as we say in calculus), but never really reaches zero, although, for practical purposes, eventually the amount remaining becomes so small it can no longer be detected. Of course, real radioactive materials don't have half lives conveniently equal to exactly one year and we don't always measure them exactly one half life apart. What would happen, for example, if we had a radioactive material that had a half life of 5.378 years and initially measured 46.305 g of it? Could we calculate how much of it would be left 1.362 years later (less than one half life)? Yes. It would be slightly more complicated but anyone with the proper math background could calculate it. The relevant equation is A = A(0) × e^(-kt), where A is how much is left after the seconds (the second, not the year, is the official unit of time in the metric system), A(0) is how much you originally measured at t=0 seconds, and k is the *decay constant* of the radioactive material. It turns out k = (ln 2)/(half life measured in seconds). In my particular example, k = 4.084 × 10^(-9) s^(-1) t = 4.298 × 10^7 s, so A = 38.850 g. This means of the original 46.305 g, 38.850 g is still left after 1.362 years, which makes sense since less than half the material has decayed since it hasn't been one half life yet. The fact that one can accurately calculate radioactive decay rates without waiting for a half life to pass is important. Uranium-238 has a half life of 4.5 billion years, but we accurately calculate how much of it will decay even in less than one second using the first-order decay formula. We don't have to wait 4.5 billion years to understand how uranium decays. Admittedly, the amount that will decay in, say, one second is very, very small, but we can accurately measure it. In fact, in my AP Chemistry classes, I frequently gave as a test question to the 17 and 18 year olds in that class a question like this: How many atoms of U-238 will decay in exactly 1 second if you have 3.74 g of it? A very doable problem, but I won't show that solution here. The point is, it can be done by bright, motivated teenagers who were really taught some science. Reply #480. Feb 15 21, 11:44 AM |
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