Why we can't see an atomic nucleus

 kw: speculative musings, calculations, photon energies, resolution

Looking at a small, old photograph made with a Brownie box camera in about 1950, I asked my father, "Can we take a picture of this picture and blow it up real big, so it is clearer?" He said, "The grain of the film would be magnified, not the details in the original scene." A few years later, using a slightly-better-than-a-toy microscope, I designed an "expander", a device with a couple of lenses that attached above the eyepiece to enlarge the image even more. I wanted to see things at 2,000X, and the microscope was limited to 400X (which is pretty good, actually). To my surprise, while the image was indeed five times as large, no more detail was visible. It was just fuzzier.

With more time and study I learned that the maximum practical magnification of an optical microscope is 800X, for someone with normal vision. Using higher magnification (up to 1,600X is available with many higher quality microscopes) makes it a little easier to see the details that are barely visible at 800X, but doesn't bring more details into view. Why is this? It comes down to the nature of light. The basic concept is that you need a "probe" smaller than the finest detail you want to see. To see bacteria, light is good enough, but to see smaller details, something smaller is needed. An atom is 10,000 times smaller than a small bacterial cell, and atomic nuclei are 100 million times smaller. We'll go step by step.

The visible spectrum is a narrow range of wavelengths of light, and you may have read that the range is from 400 nanometers (nm) at the blue end to 700 nm at the red end. These numbers are rounded off; for most people, the deepest violet (or "bluest blue") that is visible has a wavelength near 380 nm, and the "reddest red" visible is at about 750 nm. Our color vision is most sensitive to green light with a wavelength near 555 nm. This is used to calculate the highest practical magnification of microscopes. Using a bluish (sky blue, not deep blue) filter with an optical microscope reduces the fuzziness induced by longer wavelength light: red and orange are not eliminated, but reduced, making the image a bit clearer.

Articles abound regarding the ultimate resolution of microscope (and telescope) optics. Without getting into lots of equations, we can jump to the conclusion that a practical limit for most optical systems is about equal to half the wavelength of the illumination. Thus, in visible light, objects smaller than about 277 nm, or 1/3600th of a millimeter, cannot be discerned.

A second critical factor is the resolution of the unaided eye ("naked eye"). The definition of 20/20 vision is based on optical resolution of one arcminute, or 1/60th of a degree. This is sometimes stated as the ability to see lines spaced 1/10th mm apart at "reading distance"; if you do some figuring, that means "reading distance" is about 13.5 inches or 340 mm. I just held a book where I normally do for reading and measured 14 inches, so that's about right.

The ratio of 1/3600 to 1/10 is 360. How, then, can a microscope have useful magnification as high as 800X? Most microscope objective lenses are "stand-off" lenses, which sit a little farther from the subject than the diameter of their front lens. Special lens arrangements with a front lens at least twice as large as the lens-to-subject distance, used with oil between the lens and the object, can more than double the resolution, so the effective ratio gets into the range of 720 to 800. This is adequate to see bacteria such as E. coli, which are about 1/1000 mm in diameter and 2-3 thousandths of a mm long. At 800X, they would appear 0.8 mm in diameter and around 2 mm long "at reading distance". This is as far as an optical microscope can take us.

My original question was about seeing an atomic nucleus. First let's take a step in that direction and consider seeing atoms. A typical atom has a size of one or two tenths of a nanometer. That's about 1/10,000th the size of an E. coli bacterial cell. What kind of light can see that? To see atoms we need a wavelength of a tenth of a nanometer. Or less. Less is better. What kind of light does that?

To go further, we need an equation that relates photon energy to its wavelength. The standard form of this equation is

E = hc/λ

The symbols are

• E is photon (or other particle) energy
• h is Planck's constant (an extremely small number)
• c is the speed of light (an extremely large number)
• λ is the wavelength

Combining h and c in units consistent with energy in electron-Volts and wavelength in nm, this equation simplifies to

E = 1239.8/λ, and its converse, λ=1239.8/E

For our use, we can round 1239.8 to 1240. The electron-Volt, or eV, is a useful energy unit for dealing with light and with accelerated particles, such as the electrons we will consider momentarily. We find that blue light photons at 400 nm have an energy of 3.1 eV and red light photons at 700 nm have an energy of 1.77 eV. That is enough energy to stimulate the molecules in the retina of the eye without doing damage. Shorter wavelengths, with higher energy, such as ultraviolet, are damaging, which is a good reason to wear sunglasses outside.

What is the energy of a photon with a wavelength of 0.1 nm? It is 12,400 eV, often written 12.4 KeV. These are X-rays. The trouble with X-rays is that they are very hard to focus. Fortunately, because wave-particle duality applies to matter particles as well as to photons, the electron microscope was invented. Electrons can be easily turned into a beam and focused. Over time, electron microscopes were improved to the point that atoms can now be imaged directly.

This image was made with an electron microscope using an electron energy of 300,000 eV, or a wavelength of about 0.004 nm, or 4 picometers (pm). It shows a grain boundary between two silicon crystals. A technical detail: this is not a scanning electron microscope, which relies on electrons bouncing off the subject. This is transmission electron microscopy, or TEM, with the subject cut and polished to extreme thinness. The electrons that do bounce off scatter in all directions, and also knock electrons loose from the silicon, which makes for a messy image, but electrons that pass through ("transmit") form a good image, so TEM is best for this application.

On your screen the shortest distance between atoms should appear to be a few mm. Now consider: the nuclei of these atoms are 10,000 times smaller. What kind of probe can reach inside an atom to see the nucleus?

The wavelength of the electrons in this instrument, as noted, is 4 pm, while the size of an atomic nucleus is measured in femtometers (fm); 4 pm = 4,000 fm. That's much too big. A particle with a wavelength of 1 fm has to be very energetic indeed: 1,240,000,000 eV, or 1.24 GeV (1 GeV is one billion eV). The electron microscope that made the image above cost a couple of million dollars and is five feet high. Much of that size is needed to keep the very high voltage from sparking over and shorting out! Not to mention probably killing the operator. A billion eV is like lightning; it can jump for miles! A different kind of apparatus is needed.

Scientists probe the nucleus with large particle accelerators that cost many millions, or billions, of dollars, euros, whatever. They seldom use electrons. The electron is a light particle, and boosting it to energy greater than a billion eV is hard. The maximum seems to be 50 GeV. Using heavier particles, usually protons, works better. However, as the image at the top of this post implies, smacking a really high energy particle against a nucleus knocks off all kinds of stuff. That is really not conducive to making a "photograph" of a nucleus. Big accelerators such as the Large Hadron Collider in France and Switzerland have huge detectors to gather the spray of "stuff" that results from smacking nuclei really hard, with particles accelerated to extreme energies: 6.5 TeV (Trillion eV) so far (A detail: both probes and targets are accelerated, in opposite directions, so the combined collision energy is 13 TeV).

This all illustrates a critical point: The smaller the things you want to see, the more energy is needed to do so, and the more it will cost. To see really small things, right down to the level of the Planck length, which is about 1/6th of trillionth of a trillionth of a trillionth of a meter, would require enough energy to create another Universe. I don't think it is wise to play with such energies!

Confront the alien within to be ready for the alien without

 kw: book reviews, nonfiction, SETI, speculative musings

Did you ever play the Birthday Game? If you have a gathering of 23 or more people, ask them, "What are the chances that at least two people here have the same birthday?" You'll get all kinds of responses, and perhaps someone who knows this already will say, "Better than half." If you're comfortable with analytical math, this website shows how the probability with 23 people is just over 50.7%. This article from Scientific American is a bit more accessible.

More generally, if you have a large number of possibilities (N) and a much larger population to sample from—for example, millions of balls numbered 1 to 10,000—, how many items must you select (S) from the large population to have a 50% or greater chance of having two of them that are the same? If you select 90 balls from the example, is there a better-than-half chance that two of them have the same number? It turns out that the crucial factor is the square root of the number of possibilities divided by about 1.2. That is:

S > (√N)/1.2

For the example, where N = 10,000, S is at least 83, and is probably 84. I said above "about 1.2" because the divisor ranges up to 1.25 as N increases into the millions or more.

This is pertinent to the question of DNA compatibility between Earth life and any life that may be found on a faraway planet, assuming that the alien life is also DNA-based. 

We can analyze it thus. The DNA codon-to-amino acid coding table has 64 DNA 3-letter codons that select among 20 amino acids, with three of the codons used for a Stop signal to the ribosome. Clearly, many or most of the amino acids are selected by at least two codons. The number ranges up to 6 for Leucine, an amino acid with a specific shape that is apparently "most dissimilar" to the others. Seven other amino acids are selected by 4 codons each.

Here is how the table looks, for most Earth life: 

What might it happen if it were rearranged? We must assume that the translations were arrived at by random processes via natural selection (or by careful design by God).

As it happens, this table is used by all eukaryotic life and nearly all prokaryotes…but not all. An article I read listed 16 minor variations used by certain rare bacterial species. This is evidence that various minor changes to the table don't automatically produce "incompatible" organisms; the 17 known DNA variations all exist on the same Earth. What of larger changes?

Some time ago I calculated that the number of possible rearrangements of this table, keeping the DNA codons in the order shown, but moving the amino acids about freely, is about 10⁷⁰, a number with 70 or 71 digits. If we keep the codons in groups of the same size as those shown, effectively rearranging just 20 grouped items, the number of possibilities is closer to 20!, or 2.43x10¹⁸. That's 2.43 billion billion. A lot.

Now let's play the birthday game with 2.43 billion billion. Its square root is 1.56 billion; divide by 1.25 to get 1.25 billion. Simply put, we would need to collect DNA from DNA-bearing species on more than a billion planets in order to have a 50% chance that some pair of them would have compatible DNA coding tables, and we'd need to sample about 10³⁵ species to have a 50% chance at an exact match. I wonder how many aliens (if there are any) use reproductive machinery that doesn't depend on DNA?

For those who think space aliens in UFO's (UAP's) are kidnapping people for genetic experiments, I suggest it'll be a long time before the aliens find a compatible species to ANY of those that might be "out there." Human-alien hybrids are out of the question.

The above represents my own musings, based partly on prior research, as I read The Alien Perspective: A New View of Humanity and the Cosmos, by David Whitehouse. Mr. Whitehouse doesn't get into any of the stuff above; that's all "me". What he does get into is a longish history of the precursors of SETI, of SETI itself, and of its successors that are ongoing. SETI, the Search for ExtraTerrestrial Intelligence, is (was?) a radio telescope-based search for radio signals emitted by intelligent beings in stellar systems close enough to our Solar system that we can receive the signals and recognize them. More recent programs look for laser signals and possibly gamma-ray signals.

The historical portion of the book is followed by increasingly speculative discussion of what might occur upon First Contact; it's nothing like what Carl Sagan had in mind, almost certainly. To my mind, a gigantic cover-up is most likely, and the author leans in that direction to a lesser extent. Unless, of course, First Contact is more like the early part of Independence Day, globally obvious. In that case we're toast anyway; no teen hacker would be penetrating the security protocols of an alien computer that is running an alien version of Windows 9,127 or (more likely!) Linux 7,704, with help files in an alien language. Let's remember, there are a few dozen human writing systems we have not yet deciphered. What kind of script could encode Dolphin or Elephant or Squid language? Alien will be far less "obvious".

The author seems to waver between the views that aliens will be benevolent or malignant. However, he then considers that we tend to project our own fears and hopes and dreams (and nightmares) upon our anticipation of First Contact and continuing contact. This portion of the book is of real value. It clearly indicates to me that we need to get our own mental house in order, or we'll be so unprepared for First Contact, whenever it may occur, that we'll destroy ourselves before any malignant aliens could do so, and with more finality than any benevolent aliens could restore. You got it, folks: In my view, First Contact will be a portent of Doom, no matter what "they" are like.

That said, I found it hard to read the book. Not philosophically, but because the poor writing kept distracting me. Run-on sentences abound, as do partial sentences. It's almost like the placement of punctuation was frequently chosen at random. Don't authors employ copy editors any more? Maybe that's considered too expensive, but it's a false economy. I know I'd charge a helluva lot to edit text I find so disconcerting. Call me a glutton for punishment; I read the whole book through anyway.