A quick flip through my students' problem sets tells me more about them than just their ability to do quantum mechanics. My greener students make good use of the reverse side of the mountain of pages their colleagues print out every day. The paper drafts and announcements on the back side often catch my eye and offer a window into a student world I don't often get to see. Of course, recycling sheets for writing is hardly a new phenomenon. Palimpsests are parchment or vellum pages that have been erased by various methods and reused. The earlier, generally chemical, methods of erasure left faint traces of the original writing on the sheets. As methods improved, and relied more on mechanical means, such as sanding with pumice, the erasure became more complete.
In my quantum chemistry class we talked about fluorescence today. A common example of fluorescence is the odd luminescence of white t-shirts under a black light. The black light is a source of UV light, which excites some of the molecules in the detergent residue (yep - that bright white shirt is not quite as clean as you think!). The molecules then re-emit light at a slightly lower energy, which happens to be in the visible, and that we perceive as an eerie glow. The glow is present even in daylight, but the amount of visible radiation emitted through fluorscence is so much smaller than what is in incident sunlight that it swamps out the effect. But it does make your whites look subtly brighter, which is why detergent companies include "brighteners" in their formulations.
So what do white shirts have to do with palimpsests? X-rays are just another form of light (albeit very high energy light) and can cause fluorescence, too. Iron in the ink is the source of the fluorescence. Researchers at Stanford have recently uncovered not only an Archimedes manuscript hidden underneath a 13th century Byzantine prayer book, but also a text by Hyperides, a contemporary of Aristotle. The discovery of this text extends the known works of Hyperides by 20%!
Field of Science
-
-
From Valley Forge to the Lab: Parallels between Washington's Maneuvers and Drug Development3 weeks ago in The Curious Wavefunction
-
Political pollsters are pretending they know what's happening. They don't.3 weeks ago in Genomics, Medicine, and Pseudoscience
-
-
Course Corrections5 months ago in Angry by Choice
A Request to Readers
In March I'm giving a talk at the American Chemical Society National Meeting in Chicago. To prepare for the talk, I'd like to know more about my audience beyond what I can get from technorati and StatCounter. If you're a regular reader, can you tell me what is interesting about this blog? Do you learn anything from it?
Thanks!
Thanks!
Half-awake, half-life
I had a moderate allergic reaction to peanuts last night. I took diphenhydramine (Benadryl) and the hives had subsided by this morning. Lecturing on perturbation theory was more challenging. I felt like I was walking in a fog. Which got me to wondering, just what was the half-life of Benadryl? Benadryl has a relatively long half-life, between 8 and 10 hours. A typical 50 mg dose leads to a peak blood level of around 80 nanograms/ml. Most people feel drowsy at blood levels around 30 nanograms/ml. Assuming first order kinetics apply to the breakdown/elimination of Benadryl, a 30 nanogram/ml is not unlikely 10 to 15 hours later. Which would certainly explain my fogged state this morning! But not so foggy as to be unable to work the kinetics....
The Sticking Point - or Weird Words of Science 11: Eutectic
It would be an understatement to say that my youngest son is not looking forward to his annual flu shot. Last week, the Philadelphia Inquirer had a piece on helping kids cope with the pain of immunizations. Son was not particularly impressed with the advice, but he noticed that they refered to a cream which could be applied to diminish the pain of injections. "What is it, Mom?" "EMLA, I think." "EMLA?" "A eutectic mixture of local anesthetics..." Somewhere around mixture, I think I lost him!
What is a eutectic mixture? Eutectic comes from the Greek eutektos for "easily melted"(any resemblence to tectonic is, I believe, purely accidental - tectonic also comes from the Greek, but for building, not melting!). An eutectic mixture is one in which the melting point of the mix is lower than the melting point of either of the components. The binary phase diagram has a "eutectic point". EMLA is a mixture of equal weights of lidocaine and prilocaine, made into an emulsion.
It's apparently quite effective, but requires a lead time of several hours (and the foresight to ask the pediatrician for a prescription!).
What is a eutectic mixture? Eutectic comes from the Greek eutektos for "easily melted"(any resemblence to tectonic is, I believe, purely accidental - tectonic also comes from the Greek, but for building, not melting!). An eutectic mixture is one in which the melting point of the mix is lower than the melting point of either of the components. The binary phase diagram has a "eutectic point". EMLA is a mixture of equal weights of lidocaine and prilocaine, made into an emulsion.
It's apparently quite effective, but requires a lead time of several hours (and the foresight to ask the pediatrician for a prescription!).
"What was to be demonstrated" needed to be demonstrated!
A student in my office hours today asked me what the term QED meant at the bottom of a page, and got a (very short) lesson in Latin. Quod erat demonstrandum, "what was to be demonstrated", is a translation of the Greek hoper edei deixai used by Euclid to close a proof. Modern mathematical publications often substitute other symbols, including a or simply note: proven.
Orion brandy anyone?
I'll admit to being a Trekkie at some time in my life, but Dr. McCoy's stash of Saurian brandy aside, there is alcohol in interstellar space. More than 120 molecules and ions -- including ethanol -- have been identified by radioastronomers in interstellar space. The transitions between different molecular rotational states give rise to very specific lines, which can be used as molecular fingerprints.
The lines which helped identify ethanol are rotations around the carbon-carbon single bonds, rather like little propellers turning. The lines arise from vicinity of the Orion Nebula (a mere 1500 light years away), which can be seen just under Orion's belt.
The lines which helped identify ethanol are rotations around the carbon-carbon single bonds, rather like little propellers turning. The lines arise from vicinity of the Orion Nebula (a mere 1500 light years away), which can be seen just under Orion's belt.
Isotope Counts
In my quantum chemistry class we are exploring molecular vibrations. The characteristic frequency of vibration depends on the masses of the atoms in the vibrating bond. Not every student in my class is a chemist, a fact that was driven home when I assigned a problem asking students to compute the fundamental vibrational frequency of an molecule with a deuterium atom.
Most elements have several naturally occuring isotopes - forms of the element which have the same number of protons,but varying numbers of neutrons. For example, the most abundant form of the element carbon has a mass number (the sum of the number of protons and neutrons) of 12. One percent of carbon atoms, however, have an extra neutron and a mass number of 13. Carbon-14 has two extra neutrons, and is radioactive. Chemists often use isotopic substitution as a way to "tag" molecules (particularly if the isotope is radioactive).
Deuterium is an isotope of hydrogen - much of its chemical behavior is exactly the same as that of hydrogen,it just weighs more, twice as much to be precise. Unlike other elements, where the isotopes are designated by their usual name plus their mass number, isotopes of hydrogen get their own names. Deuterium has a mass number of 2, tritium a mass number of (surprise) 3. Tritium is radioactive and has a half-life of around 12 years.
In 1955, in his novel "The Mouse that Roared", Irish writer Leonard Wibberly coined "quadium" for hydrogen-4, which at the time had not been made. Since then, hydrogen-4 has been created. It is a fleeting species, its half-life is just over 10-22 seconds!
Most elements have several naturally occuring isotopes - forms of the element which have the same number of protons,but varying numbers of neutrons. For example, the most abundant form of the element carbon has a mass number (the sum of the number of protons and neutrons) of 12. One percent of carbon atoms, however, have an extra neutron and a mass number of 13. Carbon-14 has two extra neutrons, and is radioactive. Chemists often use isotopic substitution as a way to "tag" molecules (particularly if the isotope is radioactive).
Deuterium is an isotope of hydrogen - much of its chemical behavior is exactly the same as that of hydrogen,it just weighs more, twice as much to be precise. Unlike other elements, where the isotopes are designated by their usual name plus their mass number, isotopes of hydrogen get their own names. Deuterium has a mass number of 2, tritium a mass number of (surprise) 3. Tritium is radioactive and has a half-life of around 12 years.
In 1955, in his novel "The Mouse that Roared", Irish writer Leonard Wibberly coined "quadium" for hydrogen-4, which at the time had not been made. Since then, hydrogen-4 has been created. It is a fleeting species, its half-life is just over 10-22 seconds!
Strands of Life
The Nobel prize in medicine and physiology today went to two American scientists, Andrew Fire and Craig Mello, for their work on gene silencing and double-stranded RNA. When we think double-stranded, we often think of another pair of Nobel laureates (Watston and Crick) and a related molecule, DNA. RNA indeed is typically single-stranded, and uses a modified set of bases relative to DNA, subsitituting uracil for thymine. (Wikipedia has a nice diagram.)
The double-stranded version, dubbed RNAi, interferes with the decoding of genes in cells, hence the "gene-silencing" tag.
A colleagues hazards that Nobel winners are getting younger every year. Is it because the time between discovery and award is shrinking or is it that younger scientists are making more critical discoveries?
The double-stranded version, dubbed RNAi, interferes with the decoding of genes in cells, hence the "gene-silencing" tag.
A colleagues hazards that Nobel winners are getting younger every year. Is it because the time between discovery and award is shrinking or is it that younger scientists are making more critical discoveries?
Girls Don't Like Hard Science
John Tierney had an op-ed piece in the NY Times on Tuesday about the recent National Academy of Sciences report on bias toward women in science. He dismisses their findings of bias, and pins the reason for the underrepresentation of women in research universities on "they don't want to". Most girls, he opines, like the soft sciences, because they are concrete and people oriented, while boys prefer the abstract and "things". Perhaps, but you can be movivated by the concrete, be people oriented and still do "hard science". Check out the letters in response to his piece (full disclosure, one of the letters is mine). Martha Pollack's response regarding engineering was wonderful - people oriented hard science exists.
Royal Purple Molecules
My quantum mechanics class had a problem last week aimed at figuring out the color of a porphyrin molecules. Porphyrins are nitrogen-containing ring shaped chelating molecules (here is a picture) and are ubiquitous in biological systems. An iron bound to a porphyrin is the heme in hemoglobin, when a magnesium is bound, it is a key piece of chlorophyll.
The color of porphyrin should not be a mystery, as long as you know some Greek. The name comes from the Greek for purple, and indeed these compounds have vivid red-violet hues.
I asked the students to compute the energy needed to excite one of porphyrin's 18 pi electrons from the highest occupied level to the lowest unoccupied level, assuming that they could model the compound as 18 independent electrons trapped in a square 1000 pm on a side. The answer in the back of the book gave the absorbtion wavelength of 588 nm, which is precisely what you would expect for a purple compound (absorbing visible yellow light). It seemed too good to be true, for such a simple model to give such a good anwer and it was! There is an error in the answer, and the actual value is not in the visible at all, suggesting that the porphyrin is colorless!
The problem was an apt one for me to be grading this morning, as I was waiting to donate some of my own hemes in the form of whole blood at the college's blood drive.
The color of porphyrin should not be a mystery, as long as you know some Greek. The name comes from the Greek for purple, and indeed these compounds have vivid red-violet hues.
I asked the students to compute the energy needed to excite one of porphyrin's 18 pi electrons from the highest occupied level to the lowest unoccupied level, assuming that they could model the compound as 18 independent electrons trapped in a square 1000 pm on a side. The answer in the back of the book gave the absorbtion wavelength of 588 nm, which is precisely what you would expect for a purple compound (absorbing visible yellow light). It seemed too good to be true, for such a simple model to give such a good anwer and it was! There is an error in the answer, and the actual value is not in the visible at all, suggesting that the porphyrin is colorless!
The problem was an apt one for me to be grading this morning, as I was waiting to donate some of my own hemes in the form of whole blood at the college's blood drive.
Weird Words of Science 10: Eigenvalue
We're looking at the Schrödinger equation to start the term in physical chemistry. It is, of course, an eignevalue equation. The term is really a pastiche of German and English, or perhpas a quasi-translation of the German term, eigenwert. The prefix "eigen" is best translated for quantum mechanics as "characteristic". Chemists often use the eigenvalues to "characterize" or "classify" the wavefunctions or states of a systems. For example, the 1s orbital takes its designation from two eigenvalues of the wavefunction: n=1 and l=0.
"Among those ... trying to acquire a general acquaintance with Schrödinger's wave mechanics there must be many who find their mathematical equipment insufficient to follow his first great problem to determine the eigenvalues and eigenfunctions for the hydrogen atom. " Nature 23 July 192
Culture of Chemistry returns with the new term!
"Among those ... trying to acquire a general acquaintance with Schrödinger's wave mechanics there must be many who find their mathematical equipment insufficient to follow his first great problem to determine the eigenvalues and eigenfunctions for the hydrogen atom. " Nature 23 July 192
Culture of Chemistry returns with the new term!
Weird Words of Science 9: Tooth and Claw - Chelation
Orac has been posting about the abuse of chelation therapy for treating autism and other disorders. So what's a chelate and how does it work to remove metal ions from the body? EDTA is shorthand for ethylenediamminetetraacetic acid, which has the structure shown at the left. The disodium calcium salt of EDTA is the usual chemotheraputic form. Lone pairs of electrons on the nitrogens and oxygens of the EDTA (tagged blue and red in the photo) latch onto the metal. This Lewis acid-base reaction results in the metal being sequestered inside the EDTA molecule. Tucked away inside the EDTA, the metal can't accumulate in the body's tissues and is eventually eliminated. EDTA has different affinities for different metal ions, but is a pretty effective scavenger of most metal ions, including iron and calcium. Removal of too much calcium can result in cardiac arrest, so EDTA is not without safety isses, as Orac points out!
The word chelation come from the Greek for claw. Molecules that attach to metals at multiple points, like EDTA, are called multidentate ligands from their capacity to "bite" onto the metal. EDTA makes a hexadentate metal-ligand complex (6 points of attachment) with some ions, a pentadentate complex with others.
Weird Words of Science 8: Ligands, the ties that bind
Many transition metals react with bases (such as ammonia) to produce beautifully colored transition metal-ligand complexes. The word ligand comes from the Latin ligare which means to tie or bind. The same root leads to ligaments, which tie your bones together.
The photo shows green Ni(H2O)62+ and blue green Ni(NH3)62+. The ligands are water and ammonia respectively, "tied" to the Ni(II) center. The ligands form an octahedron around the metal center.
Trojan Horse Molecules: Penicillin
Penicillin was one of the first antibiotics in wide use. It was discovered in the late 19th century by a French medical student (Ernest Duchesne), though his work was never pursued. Fleming independently discovered the antibacterial activity of Penicillium mold derivatives in 1928. The active molecule was difficult to extract. The compound was finally synthesized in 1957 by John Sheehan, a chemist at MIT. This feat was made possible by the determination of penicillin's structure in 1944 by Dorothy Crowfoot Hodgkin, an X-ray crystallographer who won the 1964 Nobel prize in chemistry for that discovery and many others (including B-12 and insulin).
How does penicillin work? It is a Trojan horse molecule. Penicillin disrupts the synthesis of bacterial cell walls, thus inhibiting the bacteria's reproduction. The enzyme responsible for assembling the cell walls picks up penicillin, thinking it can incorporate into the wall. Unfortunately for the bacteria, the penicillin molecule opens up and destroys the enzyme's ability to function.
The key step in this sneak attack is the nucleophilic attack of the enzyme onto an electrophilic site on the four-membered β-lactam ring. We've been discussing these reactions in my general chemistry class this week.
Watch this webcast if you want to see how the reaction works and learn a bit about nucelophilic reactions.
Elemental Tales: Get the lead out!
Workers manufacturing the pigment white lead (Pb(OH)2.2PbCO3 apparently made a habit of adding dilute sulfuric acid to their drinking water to prevent lead poisoning. The reaction of the sulfate ions (SO42-) with the aqueous lead ions (Pb2+) forms an insoluble precipitate of lead sulfate, effectively removing the lead from the water (as long as you let the precipipate settle before drinking!). This risk of lead poisoning in these workers was so high that it was referred to as "painter's colic".
van Gogh's Palette
In an attempt to brighten a dreary Philadelphia day, I pulled out a coffee mug that glows with Vincent van Gogh's sunflowers. Among the most vivid of his favorite pigments is chrome yellow. Chrome yellow was first isolated from a natural source (the mineral crocoite) in the late 18th century by Parisienne chemist Vauquelin. By the late 19th century, when van Gogh's sunflowers took form, the vibrant yellow was one of a series of new and exceptionally vivid colors. Chrome yellow is actually a lead salt, lead chromate (PbCrO4. The pigment isstill used today but it has been replaced in many cases by similarly colored, less toxic organic pigments. Unfortunately chrome yellow degrades over time, so that the once brilliantly glowing sunflowers now appear to be dry, drab ocher shadows of van Gogh's vision.
Perhaps influenced by the mug, this week's webcast general chemistry example problem is based on a simple inorganic synthesis of the chrome yellow pigment. One of my colleague's uses another synthesis. in her course on "The Stuff of Art"
Read more about the history and chemistry of color in Bright Earth: Art and the Invention of Color by Philip Ball.
Perhaps influenced by the mug, this week's webcast general chemistry example problem is based on a simple inorganic synthesis of the chrome yellow pigment. One of my colleague's uses another synthesis. in her course on "The Stuff of Art"
Read more about the history and chemistry of color in Bright Earth: Art and the Invention of Color by Philip Ball.
Making a Mark
My interest in MRI has become less academic. I need an MRI of my hand. The orthopedic surgeon noted in passing that they will mark the spot of interest with a capsule of vitamin E, in the same way that they use lead markers in X-rays. I wondered what was so special about the vitamin E that left a trace in the MRI. Turns out that the spin-lattice relaxation time (T1) of the H's in tocopherol's chain of -CH2s is very short, and provides a high intensity signal which can be used to mark the spot. Mineral oil will work, too, but the vitamin E capsules are convenient.
A Magnetic Moment
The Culture of Chemistry welcomes 2006 - now that the grading is done and vacation has begun for me in earnest.
Graham at "Over My Med Body" notes that the total radiation dose in a year from natural background sources is much larger than the dose from any single test. He notes that ultrasound and MRIs are exceptions: ultrasound uses sound waves, and MRIs use magnets. What exactly do those magnets do?
The nuclei of many atoms have "spin" states. Like quarks which have a property called by physicists "color" but are not actually different colors like socks, spin is an instrinsic property of nuclei but this does not necessarily mean that the atoms are spinning like the earth! Hydrogen atoms, of which there are many in the human body (more than 10 pounds worth) have two spin states. Not every atom has multiple spin states. Carbon-12 (the most common form of carbon) has only one spin state. So what happens in an MRI? Radiation (yes, radiation, just very, very low energy radiation) in the form of radio waves forces the hydrogen nuclei to change state to the higher energy spin state. The time it takes for the hydrogens to relax to their low energy spin state is measured. There are two ways for the hydrogen atom to "lose spin", one is called spin-lattice relaxation (T1), the other is spin-spin relaxation (T2). Hydrogen atoms in different environments relax at different rates. Hydrogens in fatty tissue, for example, have very different relaxation times than watery tissue.
So if the changes happen because of radiation, what are the magnets for? It turns out that the separation between spin states depends on the magnitude of the magnet field, as well as the magnetic moment of the nucleus. In the earth's field, the energy between spin states is too small to do the trick of exciting them up to the higher energy state and watching them fall down. You need a high magnet field to do this.
Graham at "Over My Med Body" notes that the total radiation dose in a year from natural background sources is much larger than the dose from any single test. He notes that ultrasound and MRIs are exceptions: ultrasound uses sound waves, and MRIs use magnets. What exactly do those magnets do?
The nuclei of many atoms have "spin" states. Like quarks which have a property called by physicists "color" but are not actually different colors like socks, spin is an instrinsic property of nuclei but this does not necessarily mean that the atoms are spinning like the earth! Hydrogen atoms, of which there are many in the human body (more than 10 pounds worth) have two spin states. Not every atom has multiple spin states. Carbon-12 (the most common form of carbon) has only one spin state. So what happens in an MRI? Radiation (yes, radiation, just very, very low energy radiation) in the form of radio waves forces the hydrogen nuclei to change state to the higher energy spin state. The time it takes for the hydrogens to relax to their low energy spin state is measured. There are two ways for the hydrogen atom to "lose spin", one is called spin-lattice relaxation (T1), the other is spin-spin relaxation (T2). Hydrogen atoms in different environments relax at different rates. Hydrogens in fatty tissue, for example, have very different relaxation times than watery tissue.
So if the changes happen because of radiation, what are the magnets for? It turns out that the separation between spin states depends on the magnitude of the magnet field, as well as the magnetic moment of the nucleus. In the earth's field, the energy between spin states is too small to do the trick of exciting them up to the higher energy state and watching them fall down. You need a high magnet field to do this.
Subscribe to:
Posts (Atom)