Science Clock Series: Part II

In part two of this series, we look at a subject from nuclear physics. Or chemistry. It's kind of at the point where the two overlap.

Today's number is two, and it is approximately equal to:

\[2\approx\text{T}_{1/2}\,^{237}\text{Np}\,(\times10^6\,\text{y})\] T\(_{1/2}\) refers to the half-life of a substance, which means the amount of time, on average, that it takes for half of a sample of a radioactive substance to decay into something else. \(^{237}\)Np is the chemical symbol for the element neptunium (specifically, the isotope neptunium-237), and “\(\times10^6\)” is scientific notation for “multiply this number by 1,000,000”. So the whole expression means “approximately equal to the half-life of neptunium-237 when multiplied by two million years,” referring to two.

Neptunium is the element with atomic number 93 and the first transuranic element. This means it is the first element after uranium (atomic number 92), and is thus only found in nature in extremely tiny amounts (after uranium no element is found in nature in anything other than trace amounts). Neptunium has at least nineteen known isotopes, of which the most stable is neptunium-237 (also written \(^{237}\)Np) with 93 protons, 144 neutrons, and a half-life of 2.144 million years.

So the full expression can be read as “two (million years) is approximately equal to the half-life of neptunium-237.” And now you know where it comes from. Check back next time for something from cosmology! Click here to jump directly to it.

As an aside, the name neptunium comes from the planet Neptune which follows the planet Uranus out from the Sun, just as neptunium follows uranium in the periodic table. (Plutonium also follows neptunium just as Pluto follows Neptune [most of the time, anyway].) Uranium was named after the seventh planet from the Sun, which is now known as Uranus, but which was not always the case. When it (the planet) was originally discovered there was some controversy over what it should called: Herschel, the discoverer, wanted “Georgium Sidus” (“George's Star” in Latin), after his patron King George III of England. Astronomers from other countries were (understandably) a bit miffed at a celestial object bearing the name of a foreign monarch, and several alternate names were proposed, including "Uranus" by the German astronomer Johann Bode, who first determined Uranus' orbit. A few years later when Bode's colleague Martin Klaproth discovered a new metal (in 1789) he named it uranium in support of Bode's proposed name (which eventually beat the competition to become the standard today). By the time neptunium was discovered (officially in 1940) the name Uranus was long the standard, so neptunium and later plutonium were simply nice additions. 

The Health Benefits of Radium, or: Why you Should Look Critically at Modern Health Fads.

Today I'd like to write about one of the scarier things I know of: the radiation health fad of the early 1900's. You see, back around a hundred years ago radiation had just been discovered by the pioneering efforts of such scientific greats as the husband-and-wife team Pierre and Marie Curie and Henri Becquerel, but it was still such a new phenomenon that no one knew about the dangers it posed.

Due to radioactive decay in the bedrock that underlies them, many hot springs famed for their healing powers have traces of radon gas in them, and thus higher than average radioactivity. Given how little was known about radiation at the time, it wasn't long before a whole health fad industry sprang up in order to get more of this obviously wonderful radiation to the masses (it reminds me quite a bit of the whole ozone health fad that was in vogue around that time, but that's a topic for another time). One of the earlier products introduced was called Radon Water, bottles of water with radon dissolved it it marketed to the average person who wanted to get in on this new healthy product. Unfortunately, there's a slight problem: the longest-lived isotope of radon has a half life of just 3.82 days, so by the time the bottled water had reached its destination, quite a lot of the radioactivity would be gone.

Nothing daunted, the new start-up Radium Ore Revigator Company came up with a solution to this problem. The dilemma is that radon, being a product of the decay of other elements (notably thorium), is constantly being created but decays too rapidly to really be practically brought to market. The Radium Ore Revigator Company's answer? Instead of bringing the radon to the customer, bring the radioactive elements to them and let them produce their own radon! Thus the Revigator was born.

The Radium Ore Revigator is essentially a large water cooler lined with carnotite, an ore of uranium (and thorium, which uranium decays to) that slowly undergoes radioactive decay to produce radon. The intent was that water would be placed into the Revigator overnight to acquire a healthy dose of radon, then imbibed the next day in order to get as much radioactivity into the user as possible.

 Today, we know that radioactivity in the body is entirely a bad thing, causing cell death or cancerous mutations. It's easy to look back at the thousands (yes, thousands) of Revigator buyers in the 20's and 30's and wonder how they could be so deluded. But the scary part, for me, is that mankind really has not advanced much further today. If you read any of the materials put out by the Radium Ore Revigator Company, they sound eerily similar to claims by many different groups today. You can substitute “radio-activity” with the name of many products today and hardly notice the change. One pamphlet of theirs can be found here. For instance, you can find this little gem of a quote on page 10:

Is radio-activity dangerous to the health? Most everyone offers this questions [sic] because it is only natural to regard this as a drug or medicine. The answer is that radio-activity is not a medicine or drug, but a natural element of water, and that since practically all spring and well water that Nature herself gives for drinking purposes contain this highly effective beneficial element, it is but common sense to restore it to water that has lost it just as we restore oxygen to a stuffy room by opening a window-by eating foods that contain vitamins-or by the installation of window glass that permits the entrance in sun light of the all important ultra violet rays. The United States Government says that the radio-activity of natural water is never strong enough to be injurious. 

 I love the implicit assumption that “It's natural, therefore it must be good for you”. Sure, it's natural, but so are arsenic, cadmium, and mercury. For that matter, so is the mutation-causing ultraviolet light whose effects are compared to those of oxygen and vitamins (!). If you read the whole booklet it is both funny and terrifying, knowing what we do about radioactivity today.

I said before that I don't want to be too hard on the buyers of back then. They simply didn't know what we do now. I also don't wish to be too hard because we today are no better, really. There are many different alternative medicine products out today that we really don't know much about at this time, yet which are selling quite well. I'm not going to claim that all of them are completely without value; they might be, but we really don't know. This is partly because current federal law (the Dietary Supplement Health and Education Act of 1994) prohibits the Food and Drug Administration from testing the health claims of most alternative medicines. Thus the companies that produce these products can continue to market them without ever having to provide proof of their efficacy, while the Placebo Effect guarantees that at least some of their buyers will report improvement.

And that I suppose is really what scares me most. If people can be taken in by such things as the health benefits of radiation before, what's to stop it from happening again? Those who do not study history are doomed to repeat it, so the saying goes, and who's to say how many current health fads will be deemed to be dangerous in fifty years?


I'd like to gratefully acknowledge my inspiration for this post, the incredibly awesome chemistry website www.periodictable.com. Seriously, go check it out. You can find pictures of actual Revigators under radium (atomic number 88), and a picture of a bottle of “Radithor” Radon Water under thorium (atomic number 90). You can also read the much-better-quality article that directly inspired this post and from which a good part of my information comes there.

Burning questions of a Saturday morning.

So there I was lying in bed this morning, still half-asleep, when I got to pondering the fact that I, like the atoms that compose me, am made up of 99.99% empty space. I then idly contemplated the fact that most of this mass was in the nuclei of my atoms, at which point I was seized by a burning desire to find out how much all the electrons in all the atoms of my body put together weighed.

I know that last I checked, I had a mass of approximately 60 kg (my weight is left as an exercise for the reader), and a little searching on the 'net produced a table with the percent-by-mass composition of an average person. Starting with the first entry in the list, I have around \(61.35\text{%}\cdot 60\ \text{kg} = 36.81\ \text{kg}\) of oxygen in me. That's 36,810 grams of oxygen. A mole of oxygen being 16.00 grams, that's almost exactly 2,300 moles of oxygen in me.

(A mole, in chemistry, is simply a very large number \(-\ 6.022\times10^{23}\), to be exact. The conversion between grams and moles is pretty easy; if you have an amount of a substance equal in grams to the atomic weight of one atom (or molecule) of that substance, you have one mole of that substance, i.e., \(6.022\times10^{23}\) atoms (or molecules) of the substance. Since the atomic weight of oxygen is 16.00 atomic mass units, one mole of oxygen is 16.00 grams of oxygen. One more of oxygen at \(0^\circ\)C and normal atmospheric pressure would occupy about 22.4 liters, or just under 6 gallons.)

Now, each oxygen atom comes with 8 electrons in tow, \(8\) electrons \(\times\) \(2,300\) moles \(\times\) \(6.022\times10^{23}=1.11\times10^{28}\) electrons.

That...is a very large number. (11.1 billion billion billion).

And that's just the first element on the list! (Although, by virtue of its nature, it is likely to provide the largest number of electrons.) Next up is carbon, which, at 22.83%, comprises 13.70 kg of me. Dividing by 12.00 grams per mole, and multiplying by 6 electrons to each carbon atom, we arrive at \(3.09\times10^{27}\) electrons from carbon, a factor of 10 less than from oxygen (not surprisingly).

Since the procedure is relatively boring, and quite simple, I will spare you further talk and simply list the amounts in the table below:

---

oxygen        36.81 kg  \(1.11\times10^{28}\) electrons

carbon        13.70 kg  \(3.09\times10^{27}\) electrons

hydrogen      6.00 kg   \(3.57\times10^{27}\) electrons

nitrogen      1.54 kg   \(4.64\times10^{26}\) electrons

calcium       0.86 kg   \(2.58\times10^{26}\) electrons

phosphorus    670 g     \(1.94\times10^{26}\) electrons

potassium     120 g     \(3.51\times10^{25}\) electrons

sulfur        120 g     \(3.61\times10^{25}\) electrons

sodium        84 g      \(2.42\times10^{25}\) electrons

chlorine      84 g      \(2.43\times10^{25}\) electrons

magnesium     18 g      \(5.35\times10^{24}\) electrons

iron          6.0 g     \(1.68\times10^{24}\) electrons

fluorine      2.4 g     \(6.85\times10^{23}\) electrons

zinc          1.8 g     \(5.00\times10^{23}\) electrons

silicon       0.60 g    \(1.80\times10^{23}\) electrons

rubidium      0.60 g    \(1.56\times10^{23}\) electrons

strontium     0.30 g    \(7.84\times10^{22}\) electrons

bromine       0.24 g    \(6.33\times10^{22}\) electrons

lead          0.12 g    \(2.86\times10^{22}\) electrons

copper        0.06 g    \(1.65\times10^{22}\) electrons

aluminum      60 mg     \(1.74\times10^{22}\) electrons

cadmium       60 mg     \(1.54\times10^{22}\) electrons

cerium        60 mg     \(1.50\times10^{22}\) electrons

barium        18 mg     \(4.42\times10^{21}\) electrons

iodine        18 mg     \(4.53\times10^{21}\) electrons

tin           18 mg     \(4.57\times10^{21}\) electrons

titanium      18 mg     \(4.98\times10^{21}\) electrons

boron         18 mg     \(5.01\times10^{21}\) electrons

nickel        12 mg     \(3.45\times10^{21}\) electrons

selenium      12 mg     \(3.11\times10^{21}\) electrons

chromium      12 mg     \(3.34\times10^{21}\) electrons

manganese     12 mg     \(3.29\times10^{21}\) electrons

arsenic       6.0 mg    \(1.59\times10^{21}\) electrons

lithium       6.0 mg    \(1.56\times10^{21}\) electrons

cesium        5.4 mg    \(1.35\times10^{21}\) electrons

mercury       5.4 mg    \(1.30\times10^{21}\) electrons

germanium     4.2 mg    \(1.11\times10^{21}\) electrons

molybdenum    4.2 mg    \(1.10\times10^{21}\) electrons

cobalt        2.4 mg    \(6.62\times10^{20}\) electrons

antimony      1.8 mg    \(4.54\times10^{20}\) electrons

silver        1.8 mg    \(4.72\times10^{20}\) electrons

niobium       1.2 mg    \(3.19\times10^{20}\) electrons

zirconium     0.60 mg   \(1.58\times10^{20}\) electrons

lanthanum     0.60 mg   \(1.48\times10^{20}\) electrons

gallium       0.60 mg   \(1.61\times10^{20}\) electrons

tellurium     0.60 mg   \(1.47\times10^{20}\) electrons

yttrium       0.54 mg   \(1.42\times10^{20}\) electrons

bismuth       0.42 mg   \(1.00\times10^{20}\) electrons

thallium      0.42 mg   \(1.00\times10^{20}\) electrons

indium        0.36 mg   \(9.25\times10^{19}\) electrons

gold          0.18 mg   \(4.35\times10^{19}\) electrons

scandium      0.18 mg   \(5.06\times10^{19}\) electrons

tantalum      0.18 mg   \(4.37\times10^{19}\) electrons

vanadium      0.12 mg   \(3.26\times10^{19}\) electrons

thorium       0.060 mg  \(1.40\times10^{19}\) electrons

uranium       60 μg     \(1.40\times10^{19}\) electrons

samarium      42 μg     \(1.04\times10^{19}\) electrons

beryllium     30 μg     \(8.02\times10^{18}\) electrons

tungsten      18 μg     \(4.36\times10^{18}\) electrons

---

(if you're wondering about the units, conveniently, 0.06 g = 60 mg and 0.06 mg = 60 μg)

If you add all those electrons up, you come up with a total of \(1.88\times10^{28}\) electrons. That's a lot of electrons -- 18.8 billion billion billion, to be exact. But how much mass do they have? And how much do they weigh?

Finding the mass is easy. The mass of an electron is \(9.11\times10^{-31}\) kg so \(1.88\times10^{28}\) of them together have a mass of 17.1 grams, which has a weight of approximately 1/25 of a pound.

Wow. All the electrons in my body make up a measly 0.0000029% of my mass. Everything else is concentrated in the nuclei of my atoms. Wild, huh?

Particles, magnets, and clothes, oh boy!

Wow! Today has been fantastically incredible for me. I'm going to have to troll my vocabulary for superlatives to fully describe my day.

Today, in case I haven't mentioned it before, is the day everyone in my Modern Physics class demonstrated their projects.  We were a little unsure about ours -- as I reported a few days ago, our attempt to run it on Friday, with every confidence that it would work, came to nothing, leaving us forlorn and distraught. However, Mike, my partner and the one with the actual equipment, ran it again on Saturday and was able to see many trails (humorously, he tried calling several people to tell them about it, including me, and they all for one reason or another didn't answer, leaving another classmate to quip "Mike discovered the secret of the universe, and nobody picked up the phone!"). So when we ran it today, we were hopeful about seeing trails. At first, it seemed our attempts would be in vain, as there was little alcohol rain and nary a trail in sight. However, after we'd seen everybody's projects and the class was over, Mike twiddled with it a bit, added some alcohol and set the base plate directly on the dry ice, and voila! Trails galore! I could hardly believe my eyes, at first -- 8 unsuccessful tries before seeing anything more than a random cosmic ray, and now, trails popping off in quick succession, even showering about en masse like sparklers at times. It was definitely one of the cooler and more dramatic things I've seen in my life.
I attempted to capture it on camera, but unfortunately the conditions necessary to see the trails made it very difficult to get a good picture of them. And still pictures can never do it justice, anyway. Nothing can compare to actually seeing subatomic particles interacting with the alcohol-vapor rich air in front of you, suddenly appearing and shooting along like a meteor, leaving a trail of droplets behind them to disperse and fall out of the air over a second or two. Or bouncing off the plastic aquarium containing them and ricocheting back into the chamber. I attach one of the better pictures I managed to take below. The trail in this picture is quite clearly visible as the white horizontal streak near the middle of the picture. The dark disk to the left is the uranium-doped sample, and the americium is just visible in the back corner as the tiny grey disk.

The intrepid Lego men, of course, are there to monitor and watch the proceedings.

All in all, it was amazing. Mike and I sat and watched it for almost half an hour, mesmerized by the interplay of fundamental forces going on in the chamber before us. The most fantastic part for me was seeing a trail split. That's right, I saw a single trail, straight as an arrow, suddenly spawn a second trail branching off at about a 30 degree angle. I'm positive it wasn't two trails that happened to be near each other, because the second trail quite clearly started at the first one, which kept on its straight course afterwards. What was it? I don't know. A decay seems unlikely, as uranium and americium both decay mostly to quite stable alpha particles (helium nuclei). I suspect, taking conservation of momentum into account, that it may have been an alpha particle knocking an electron loose off an air molecule causing said electron to go careening away.

The sub-atomic dance going on before our eyes was so beautiful, we found it a hard thing to finally have to take it down. There's a chance Mike will take it up tomorrow to Mauna Kea, where he'd have a good chance of being able to observe cosmic rays, and even the showers of secondary particles they create when they strike a molecule in the atmosphere, slamming into it at appreciable fractions of the speed of light.

I am happy to be able to say that I have finally been able to watch where atomic and subatomic particles go with my own eyes. While that was certainly intellectually satisfying, the second big attraction of my day -- magnets -- was incredible on a much more visceral level.

You see, one of the other project this morning required the use of a powerful magnet in order to split the spectral lines in a mercury vapor lamp. They were using a large cylindrical magnet -- and when I say large, I mean it had an interior diameter easily big enough for me to put my hand all the way through its 8-inch length without touching the insides. Our teacher, Dr. Takamiya, also brought along a small pair of extremely -- and I mean extremely -- powerful magnets. I only succeeded in separating them after putting one of them up against a corner of a desk and shoving laterally with all my strength against the other one. But while their strength was of an order unknown to me in magnets before, that in itself was not too incredible. I've played with strong magnets before. What was incredible, and completely blew my mind, was what happened when I moved them near the large cylindrical magnet.

I didn't have much in mind when I first got the impulse to hold the small magnets close to the large one (at this point they were bonded strongly together in my hand, generating a powerful field). I had a natural, subconscious hypothesis that I would simply feel a very powerful force pulling my hand towards the magnet. But that's not what happened -- not at all. I was snapped out of my assumptions about the behavior of magnets when the pair in my hand started to twist and turn, as if with a mind of their own. My memories of the event are lurid. I'm almost positive that I felt no actual force on the magnets, only torque. They weren't being attracted to the magnet so much as they were trying to align themselves with it field. Intrigued, I moved my hand up and down outside the magnets, and felt the magnets in my grip react as if alive, writhing about in an attempt to obey the commands of the invisible magnetic field they were being pulled through. It was surreal. I'm fairly certain I stood there with a huge grin lighting up my face for ten or twenty seconds, just feeling the thrill of magnets calling to each other across space. My astonished exclamations of delight and wonder quickly brought several other classmates to my side, so I relinquished the magnets to let them experience the wonder, while still myself able to feel their strange tugging in my hand. The memory still brings a thrill to my spine. Why could not we have done this in my Electromagnetism class this semester, at least once? A whole semester's worth of dry theorems and boring formulae was distilled into one intense, gripping, and powerful moment for me. If I had gotten to do this in January, I would have been excited to learn more about this mysterious force. As it is, I'm still excited from this morning, and jumping up and down inside at the remembrance.

Later, as people were preparing to leave, I got another chance with the magnets, so I took the cylindrical magnet and laid it on its side, then held a single small magnet in my hand and pushed it through the middle of the cylinder. I did feel a force this time, though again, it was drowned out by the overwhelming torque. Each time as I moved the magnet in and out of the cylinder, it desperately tried to flip itself around in order to line up with the field, then slowly tried to draw my hand towards the middle of the cylinder once it was inside. The whole experience was...beyond my meager ability to describe. You can only truly understand if you have felt the small metallic cylinders in your hand jerking and tumbling about with a life of their own to follow the unseen lines of force emanating from their larger cousin nearby. Truly, I must see about getting me some magnets of this caliber.

The third item on my list is nowhere near as exciting as the first two, but I needed a third noun for my title, and it warrants a mention. With summer coming on ( I can tell it's getting light a little bit earlier each week), and some of my older pairs of shorts showing their age, I finally found time today to run to Walmart and pick up two more pairs of my favoritest shorts. I know I know, not as exciting as watching bits of atoms flying about, or experiencing forces I turn out to have a surprising ignorance of, but it makes me happy none the less, and makes a fitting end for one of the most exciting days for me in quite a while. I need to finish this and get to bed  now, so perhaps tomorrow I'll tell you about the Residue Theorem, and how that's impacted my life. And about my upcoming observing run at the Institute for Astronomy on Thursday and Friday nights with Dr. Takamiya.
Till then, aloha!

Building a working cloud chamber, part 4.

Sigh...the end of the semester cannot come soon enough for me.

Homework piles upon presentation upon paper...great undulating waves of responsibility threatening to swamp me. Thankfully, I gave my presentation for Partial Differential Equations today, and it went off fine (pretty good, considering I finished assembling it an hour before and practiced not at all). Now only a few assignments remain before a breather next weekend in preparation for the four finals I have the week after that.

One of those assignments is the presenting of our cloud chamber experiment on Tuesday for our last Modern Physics class. Today we ran our cloud chamber experiment for the 4th time, with, unfortunately, depressingly null results. We we quite confident of seeing something this time, especially since one of the professors graciously loaned us a sample of uranium to use as a particle source (I've never gotten to hold real uranium before!). We got a cloud just fine, but were unable to register more than a few, questionable, tracks. We decided to flip the assembly upside down again, in order to get a less turbulent cloud, which worked, somewhat. We were able to get a cloud....it was just very thin, and didn't really show trails.  So...I think the fact that we have the setup right means we'll do fine as far as grading goes (this experiment is 15% of our grade, if I remember correctly), but it's slightly disappointing not to have been able to get irrefutable particle tracks.

Anyway, yesterday I discovered by accident that Google has finally updated the satellite imagery of my home in California (after only, what, 5 or 6 years?). In fact, I was able to see the very hut I built for my ducks a year ago. It was slightly surreal, and left me dumbfounded that something I built with my own hands could be visible FROM SPACE (to be fair, I didn't build it by myself [Dad deserves a fair share of credit], but it was my idea and pet project).

Thankfully I remain in good health overall, just harried by assignments nipping at my heels as the semester draws to a close. I don't know how much I'll be able to write in the next two weeks, but I'll try to post a short something or other to keep you all informed of how I'm doing.