The Coolest Thing You Likely Never Learned About Hydrogen

Posted on April 10, 2013 by danielfeldman

What do you know about Hydrogen? In a very un-scientific study, I decided to find out. I posed this question to my Facebook friends: “If I ask you to tell me 1 thing you know off the top of your head about Hydrogen, what would it be? The cooler the factoid the better.” I have a bunch of science and non-science Facebook friends, and got a nice spread of answers. Here’s some of them, more common ones closer the top (can you guess which answers were from science majors?):
1) It’s in water (H2O)
2) Most abundant element in the Universe
3) It’s highly flammable/explosive in air
4) It’s a proton
5) Nuclear fusion (and fusion bombs)
6) 1st on the periodic table
7) The only wavefunction we can solve exactly
8) Hydrogen bonds with certain elements strongly
9) Hydrogen in hydrocarbons when burned release greenhouse gases
10) Dr. Manhattan’s logo
11) Proton pump in mitochondria
12) H+ ions in acids
(Many more great answers, too many to include them all!)

I think these results paint a great picture of why Hydrogen is really cool, and really important. It also provides strong evidence for the assertion I put as the title of this post. Even amongst my science/astronomy friends, nobody mentioned what I think of as the coolest factoid about Hydrogen (but granted, I’m a nerdy astronomy student and I only asked for one factoid). It’s especially important to the understanding of stars and what we see when we look at the sun! I’m talking of course about the Hydrogen anion (H-). That’s right…you can have negative hydrogen, and its properties are really cool!

To understand negative hydrogen, let’s talk about some chemistry ideas. First, recall the Bohr model of the neutral hydrogen atom: you have a proton nucleus, with an electron zooming around in specific energy levels. The electron is bound to the proton because their opposite charges make them attractive…the proton holds onto it through this electrical tugging. Though this model is too basic and not exactly correct, it helps us intuitively illustrate physics fundamental to our understanding of the Universe—that when an electron jumps (transitions) between two different energy levels, light gets either absorbed (lower level to higher level) or emitted (higher level to lower level). If both of these energy levels keep the electron bound to the nucleus, we call it a bound-bound transition. Neutral hydrogen gas has many bound levels, and therefore has many bound-bound transitions (some of them corresponding to visible colors)! If the electron absorbs light with lots of energy, the electron escapes the atom completely—this is called a bound-free transition, since the electron ends up free of the tyrannical proton nucleus…forming an H+ ion!

Let there be light!

But there’s another, more wacky form of Hydrogen! Hydrogen is highly polarized, and can actually capture an additional electron, forming a negative ion. As you might expect, this ion is very weakly bound together—in fact, it only has one bound state (the ground state), and the 2nd electron can easily escape through absorption of light! Since it only has one bound state, it is impossible for H-, also known as hydride, to have bound-bound transitions. However, since it is easy to ionize (eject it’s second electron), it readily absorbs light, especially in near-infrared, visible, and UV wavelengths (and even higher energies too!).

Hydride

For those of you with a scientific fascination with awesome atomic configurations, I highly highly encourage you to delve deeper into the characteristics of this fascinating ion, but I want to focus on the reason it’s really cool/important to me (as an astronomy student). One of the places hydride shows up is in the atmosphere of the sun! The Sun is a giant ball of hot plasma—its photosphere (where most of the light escapes the sun’s surface) is around 6000 degrees Celsius—and it’s even hotter as you get deeper and deeper in. This plasma makes it difficult for light to escape the surface—it is constantly interacting with the protons and electrons, getting absorbed and scattered all over the place. In fact, despite the incredible speed of light, it can take a photon of light up to 100,000 years or more to escape! The difficulty of light to escape from a gas or plasma (like the Sun) is called it’s opacity. When something has a high opacity (more opaque), you cannot see deeper into it.

The Sun seems to have a surface—the photosphere—under which the Sun becomes very opaque. It is very hard for radiation from deeper in its atmosphere to escape…and the reason? You guessed it—the negative hydrogen ion! Hydride readily forms in the Sun’s atmosphere, so there’s a lot of it. There’s also a lot of light energy trying to escape the Sun, which encounters the H- ions. Because it’s so easy to ionize hydride, the hydride will absorb the light and the second electron escapes. This happens so much that the light has trouble punching through all the hydride ions, which keep forming to continue blocking this light. Those pesky hydride ions are therefore the major source of the Sun’s opacity! And this is not just true for the Sun, but for many many other stars as well!

Go home, photon: you're drunk!

Go home, photon: you’re drunk!

So that’s my favorite thing about Hydrogen—it’s negative ion! Was it something you learned in school? What’s your favorite factoid about Hydrogen (that you can name off the top of your head)? Leave a comment! I want to once again thank all of my wonderful friends for their great responses to my Hydrogen question—it’s amazing to see how many answers I received from different people, and the support of a somewhat silly venture of mine is always something I appreciate. Until next time, friends!

Posted in Astronomy, Physics | Tagged , , , | 6 Comments

Indiana Legislators, Waldo, and Pi

Posted on March 16, 2013 by danielfeldman

I hope everyone enjoyed their Pi Day (3/14)! I know, I’m two days late, but for good reason—I spent the last two days wondering what to do to honor pi day, and researching said topic (and doing my usual grad school duties). There’s a lot of angles I could take on pi—the controversies around pi’s usage, how pi pops up all over physics, even when circles aren’t necessarily involved, the notion that the secrets of the Universe is encoded in its digits—but I’m going to focus on a popular legend. I’m sure you, like me, have heard the story that lawmakers once tried to legally change the value of pi to 3. Likely under the guise that the Bible sets the value of pi to 3, since King Solomon supposedly built a round bathtub with a circumference of 30 cubits and a diameter of 10 cubits (although a Jewish Rabbi named Nehemiah around 150 C.E. tried to explain this discrepancy through the bathtub’s thickness…smart man). Well, this rumor isn’t true…but it’s got a real story that’s way better.

Let me take you back to the late 1800’s. In a small town called Solitude, Indiana (best wikipedia page ever…yeah, you can see where this story is going) lived a physician named Dr. Goodwin. Different sources claim his first name was Edward, others Edwin…the point is that he was an amateur mathematician working on the problem of trying to create a square whose area is exactly that of a circle. In principle this is done with just a compass and straight edge, and would make a difficult task (finding a circle’s area) much easier (area of a square). There was a big problem though…a mathematician named Ferdinand von Lindemann had already proven it was mathematically impossible to do. The reason is because pi is not just some ordinary irrational number—it’s a transcendental number—it’s impossible to calculate via a simple algebraic equation. You just can’t make a square whose sides are exactly the square root of pi in length. But darn it, Dr. Goodwin was determined, and sure enough he did it in 1894 (but not really)! It even got published in American Mathematical Monthly! Who knew mathematical papers existed, or that they were that desperate for material?

Dr. Goodwin was a real character. His books are self-published, and he even stated that God told him the value of pi in 1888 (I guess God had done some more math in between the Bible’s publishing and then). Not only did he get a proof of an impossibility published, he supposedly copyrighted it! Yeah, you read that correctly. Never mind that knowledge isn’t copyrightable (despite academic publishing, we don’t get royalties) but by Jove he did it anyway. His writings were gibberish, and anyone who claims to know how to follow his writings will tell you that you can back out his values for pi. That’s right, values. Each of his writings back out a different value of pi, including 4, 3.2325, 3.2, and even 9.2.

Well, Dr. Goodwin had a big problem. He was afraid that Indiana’s education system could not afford to pay royalties to teach his mathematical truth to the children. His beautiful discovery might be lost to ignorance—so he proposed a solution to Indiana representative Taylor I. Record: if Indiana passed a law stating this as mathematical truth, the school system would not have to pay royalties! Sound like a good plan?

Representative Record thought so. So he brought it to the floor of the Indiana legislature in 1897 (House Bill 246). Most sources I read just talked about the end result of the bill, but if you track it’s progress, you get a fascinating look into the legislative process of the Hoosier state. The bill was first forwarded to the House Committee on Canals. Yeah. They then forwarded it to the Committee on Education, a slightly better choice (though the best would be the Committee on Crap, if that even exists). Well, the Education Committee brought it to the full House floor, and recommended it pass. And it did, unanimously, 67 to 0! Yep, nobody thought this bill was a problem.

While this is going on, the papers begin to take notice. One paper, written in complete German (Der Tagliche Telegraph) chronicled how ridiculous this was, and mentioned von Lindemann’s proof…but since it was in German, nobody noticed. Instead, people read the English papers…which all supported the bill! We should be embarrassed. By the time it passed in the House, the rest of the country took notice, and Indiana became the laughing stock of the nation (that’s right, Dan Quayle was not the first to see this happen).

Now the bill had to pass the Indiana Senate. But not so fast! Enter Dr. Clarence Abiathar Waldo. Dr. Waldo was serving as the president of the Indiana Academy of Science and was the head professor of mathematics at Purdue University, and decided to take a stand against the pi bill. Yeah, Dr. Waldo saving Indiana from further embarrassment…you can’t make this stuff up!

At this point in the story, the bill had been passed to the Senate Committee on Temperance. The chairman of this committee, Senator Harry S. New, recommended the bill pass. Dr. Waldo coached a few of the Senators to speak out against the bill and recommend it die there and then. Some sources I read seem to think that it was thanks to Dr. Waldo that this bill was thrown out, others say it was decided that the Senators, all of whom admitted to not having math knowledge, thought it ridiculous to pass math legislation and threw it out on those grounds. But the point is, the bill, having now made Indiana look like the dumbest state ever, had finally found its resting place in the cemetery of defeated bills.

Our story ends here…just 5 years after his humiliating defeat, Dr. Goodwin died. History becomes legend, and now we hear ripples of this historical event in the form of pi legislation rumors. I highly recommend you guys research this story, as there are some hilarious quotes from the various senators, key players, newspapers, etc. I’ll end this belated-pi-day entry with the New Harmony, Indiana obituary for Dr. Goodwin:

“He felt that he had a great invention and wished the world to have the benefit of it. In years to come Dr. Goodwin’s plan for measuring the heavens may receive the approbation which was untiringly sought by its originator. As years went on and he saw the child of his genius still unreceived by the scientific world, he became broken with disappointment, although he never lost hope and trusted that before his end came he would see the world awakened to the greatness of his plan and taste for a moment the sweetness of success. He was doomed to disappointment, and in the peaceful confines of village life the tragedy of a fruitless ambition was enacted.”

RIP Dr. Goodwin and House Bill 246

Posted in Math, Uncategorized | Tagged , , , | Leave a comment

The Dan Feldman Wavefunction

Posted on February 21, 2013 by danielfeldman

Greetings, everyone! During my lunch break today, I was thinking about quantum mechanics (that’s what everyone thinks about while eating, right?), and started to wonder what my wave function might look like for any given day. I’ve mentioned wave functions before (see: Zeno’s Paradox), but I’ll give you a quick refresher before delving into my thought experiment.

In quantum mechanics, we usually talk about wave functions when describing the probability amplitude of the position(s) of one or more particles/atoms/molecules in space. In simpler words, it’s the likelihood of finding a particle somewhere in space at a given time. Wave functions have high values where the probability is high, and low where you are unlikely to find a particle. Before I give you an example of a particle’s wave function, let’s take a classical physics (large) example—me.

In classical physics (and our everyday lives), objects have one position at a given time. I’m currently sitting at my desk, and twenty minutes ago, I was in the bathroom. If you were to try and find me right now (i.e. measure my position), there is a certainty that you’d find me at my desk. If you were to try and find me twenty minutes ago, there’s a certainty that you’d find me on the toilet (and annoyed, you creep). The world is deterministic, because we can find where something is at a given time, and it follows the laws of physics.

What goes up...

Lets say you performed this experiment over and over again—10 times, to be exact—trying to find me during my Thursday office hours. You find me at my desk 9 times, and once on the toilet. Then my measured probability amplitude would have a value of 0.9 at my desk (I was there 90% of the time) and 0.1 at the toilet (I was there 10% of the time). For those who are interested in the mathematical form of your findings, this would be represented by two delta functions. The probability amplitude is really the square of the wave function (represented by a greek Psi squared |ψ|^2). Just some math, not that important to this entry.

But what if I was a quantum system? In quantum mechanics, wave functions technically represent the same thing—probability amplitude of your position. But it’s a little weird. Think about what I told you about my wave function. According to your experiment, you find me in one of two places…at my desk, and on the toilet. Classically (and via common sense), we know that I’m really in one place or the other at any given time…it’s just that if you do the experiment over and over, you sometimes yield different results. But I only occupy one place (or state) at a time. But in quantum mechanics, we don’t interpret this the same way. If I was a quantum system, I would be in BOTH places at the same time, but then when you look at one place (say you walk into my office), there is a 90% probability I will be there, and upon seeing me (making a measurement), my state is altered to be 100% at my desk. Weird right?

So I got to thinking…on any given day, where am I most likely to be? I’m a man of habit, and I spend most of my time in the same couple of places. So, I calculated what my wave function might look like. And here’s the results (click to enlarge):

Needless to say, I am the Mayor of that Bruegger's establishment.

If anyone can come up with a mathematical representation of this–100 points.

For those uninitiated, my office (and classes) are on the 5th floor of the College of Arts and Sciences (CAS) Building. Not the most exciting life, but I’m a first year graduate student at the moment, so it’s not all that surprising. Classically, the way you interpret this graph is thus: If you want to find me, there is a certain probability that I will be in those particular places…I’m only in one of those places at any given time, but if you were to try and find me every day, these are how many times you would find me in said places.

Quantum mechanically, as long as you haven’t gone looking for me yet (measured my position), I could be, and AM (sort of) in all of those places at the same time. I’m in what’s called a superposition of all of these states at once, and once you measure my position, I become in only one of those states. And if you do this over and over, I will be in one of those states a certain amount of times based on the probabilities in the graph. This notion is a bit absurd, and leads to the paradoxical thought experiment known as Schrödinger’s Cat (but that’s another story).

Nobody really understands quantum mechanics, or at least what the true physical nature of these wave functions is, but this is one interpretation usually accepted by physicists. It’s worth noting that in physics/chemistry, we can calculate some truly awesome looking wave functions for particles, atoms, and molecules…it’s pretty wild.

What does your wave function look like?

Posted in Physics | Tagged , | 1 Comment

Musings of Great Minds

Posted on February 15, 2013 by danielfeldman

As many of you know (perhaps from reading the ‘about’ section of this site), I am a graduate student. This means I am tasked with running discussion sections for an astronomy class–this semester a class called Cosmic Controversies, which teaches some 180 non-major students about some of the most controversial aspects of science and Astronomy. Well, some of the students in my sections have been a bit difficult to reach…or at least, to stimulate interesting and fun discussion with…and I’ve been trying to find subtle ways to spice the discussion section up in a way to get them interested. We’ve recently begun a short section on the history of Astronomy, detailing discoveries and lives of notable names in Astronomy and Physics. Notable figures that include Aristotle, Pythagoras, Hipparchus, Kepler, Aristarchus, Brahe, as well as a whole slew of others. These figures were powerful minds who spent their fascinating lives pondering and discovering the secrets of the Universe.

Well, I decided that as a way to try and spur some interest in this class, I wrote quotes I found interesting or inspiring on all of their quizzes. Maybe it won’t make a difference at all (wishful thinking is always nice), but we’ll see how it goes. If any of you readers have suggestions for stimulating interest among non-majors in a discussion section (generally, during class, etc.), feel free to leave a comment! In the meantime, since I haven’t got enough time to write a science entry here today, I thought I’d share with y’all some of the quotes I shared with my students. I highly encourage all of you to look up the lives and accomplishments of some these brilliant scientists, philosophers, mathematicians, and writers. I apologize for the lack of female minds mentioned here…don’t let it make you think women are any less brilliant. Because they are just as scientifically minded and gifted as their male counterparts.

“Mortal as I am, I know that I am born for a day, but when I follow the serried multitude of the stars in their circular course, my feet no longer touch the earth; I ascend to Zeus himself to feast me on ambrosia, the food of the gods.” – Ptolemy

“Mensus eram coelos, nunc terrae metior umbras. Mens coelestis erat, corporis umbra iacet.” (I measured the skies, now the shadows I measure/ Skybound was the mind, earthbound the body rests.) – Johannes Kepler (apparently a self-authored epitaph)

“The history of astronomy is a history of receding horizons.” – Edwin Hubble

“Bright points in the sky or a blow on the head will equally cause one to see stars.” – Percival Lowell

“E pur si muove.” (And yet it moves.) – Galileo Galilei (supposedly muttered after he recanted his beliefs to the inquisition)

“In the center of all rests the Sun. For who would place this lamp of a very beautiful temple in another or better place than this from which it can illuminate everything at the same time.” – Nicolaus Copernicus

“Nothing in life is to be feared, it is only to be understood. Now is the time to understand more, so that we may fear less.” – Marie Curie

“Astronomy? Impossible to understand and madness to investigate.” – Sophocles

“It suddenly struck me that that tiny pea, pretty and blue, was the earth. I put up my thumb and shut one eye, and my thumb blotted out the planet earth. I didn’t feel like a giant. I felt very, very small.” – Neil Armstrong

“Consider again that dot. That’s here. That’s home. That’s us. On it everyone you love, everyone you know, everyone you ever heard of, every human being who ever was, lived out their lives. The aggregate of our joy and suffering, thousands of confident religions, ideologies, and economic doctrines, every hunter and forager, every hero and coward, every creator and destroyer of civilization, every king and peasant, every young couple in love, every mother and father, hopeful child, inventor and explorer, every teacher of morals, every corrupt politician, every ‘superstar’, every ‘supreme leader’, every saint and sinner in the history of our species lived there – on a mote of dust suspended in a sunbeam.” – Carl Sagan

Who knows? Maybe you will one day be a part of one of these lists–a smattering of human brilliance and achievement. Let the lives of men and women of the past and present inspire you to build a fruitful and bright future for yourself and those around you. And remember this inspiration the next time you vote on the future of scientific funding.

Posted in Astronomy | Tagged , , | Leave a comment