The Pew Research Center (whoever they are) recently got a lot of press for a survey that compares the attitudes of scientists to attitudes of the general public.  Some agreement, some disagreement; no surprise there.

But this exercise also included a quiz on science.   And, since I have no reason to believe that people who make up quizzes know more than the general population, I took a look at it for you.   It’s 12 questions, each with four choices.  Ten of the questions are just fine: there is one obvious answer.  But one is a bit dubious.  Let’s look at it.

This question was pointed out as especially troubling in the report.  Pew said “And some high-school science knowledge is elusive for most Americans: Fewer than half (46%) know that electrons are smaller than atoms.”  But, it turns out that the question is actually testing people’s interpretation of the language as much as their knowledge of science.

Electrons are smaller than atoms:

True

False

Argument 1: Electrons (when struck by other electrons at very high energy) are point-like particles.  They show no evidence of internal structure or size.  What’s actually measured in these experiments is how one electron scatters off another.  You take a particle accelerator, shoot some electrons in at nearly the speed of light, and you have a big electron detector around the collision region.  You look for the angular distribution and velocity distribution of the outgoing electrons.

When you do that kind of experiment, it turns out that the scattered electrons come out with the same distribution of angles and velocities that you compute (via quantum mechanics) on the assumption that electrons are mathematical points that carry electric charge.   The electrons don’t really collide; rather, they repel each other, and the closer they get, the stronger the repulsion.  It is inverse-square law, all the way in.

If the electrons had a “size”, you might expect something like a hard core, where (if they get close enough), they would just bounce.    Or, perhaps the opposite: imagine that the electric charge is distributed over a little spherical region.  If so, the electrostatic repulsion would be softer — it wouldn’t rise as fast as the inverse-square law when the clouds of charge started to overlap.  Either way, you’d see a deviation from the inverse-square law that holds true at long distances, and you could call the distance where that happens the size of the electron.

But there is no deviation, so the conventional wisdom is that the electron has zero size.  And that’s true enough, for that kind of experiment.

But you can look at it another way:

Argument 2: The nucleus of an atom is a tiny little heavy thing in the center of an atom.  The rest of the atom is just a cloud of electrons.  Therefore, electrons are about the same size of atoms.

There’s nothing particularly wrong with that argument either, as long as you qualify it carefully: “electrons in atoms are about the same size as atoms.”  But, at least on Earth, most electrons are in atoms, so it’s not a bad statement.

This argument corresponds to a rather different pair of experiments.    We gently bump atoms together to see how big they are.  The energy of the collisions is rather small, corresponding perhaps to normal collisions at room temperature, where the atoms hit at perhaps a kilometer per second.  And then, there is a completely different experiment where you measure the size of the nucleus by shooting high-velocity protons at it.

Who’s right?

Well, among physicists, the conventional meaning of the question is not how big an electron normally is, but rather how small can you make it.  In the context of physics, you know that any small, light object follows quantum mechanics, and that it doesn’t have a well-defined position.    The position is uncertain, so the object (e.g. the electron) can be found somewhere inside a probability cloud, and that the size of this cloud depends very much on external circumstances.  Give it a big box and it will spread out.

But, interpret the question as normal English, it’s rather different.  Let’s look at some analogous questions:

• Birds are smaller than cows.
• People are smarter than chimps.
• Pens are more permanent than pencils.

In each case, the only reasonable choice would be “yes”.  But that is because we interpret such questions as describing the “normal” situation.   We don’t mean that all birds are smaller than all cows: ostriches are big and newborn calves are not huge.  Nor do we mean that every person, even those with severe brain damage, are smarter than all chimps.   And, under an eraser, pens are much more permanent than pencils.  But, some inks will fade in sunlight while the graphite from a pencil never will.

In this light, it is reasonable to think that “most electrons are about as big as an atom” and then be very uncertain what the correct answer should be.

So, normally, we don’t look for extreme cases like we do in argument 1.  Can we blame people for taking a more normal interpretation of the question?   (Of course, not everyone who answered “False” was thinking this way.   Doubtless, some were just completely confused or ignorant.)  But, it’s a bad question because either of the two answers are reasonable, given a reasonable interpretation of the question.

Unionized?

This reminds me of the way to tell a chemist or physicist from most anyone else in one question.    Ask them to pronounce the word “unionized” (and you should spell it out).  Chemists and physicists will interpret it as “un-ionized”, while most other humans, having more incentive to think about labor unions than ions, will pronounce it as “union-ized”.  It works every time.