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Wayne State University

Aim Higher

Jun 8 / Peter Hoffmann

The very small and the very big.

In my lab we measure what water confined in a nanometer-sized gap does when you slowly squeeze it more. Why would you want to do that, you may ask – well, let’s talk about that later. Suffice to say, we have our reasons. What I want to talk about here, instead, is how something that’s almost common place in our lab (it’s just a number on the axis of a graph), is truly astonishing once you think about. What I’m talking about is the tiny scale at which scientists (including my students) are able to perform precise measurements. What’s on the x-axis of our measurements are nanometers and, sometimes, Ångstrøms (which is a tenth of a nanometer). Within these few nanometers we are able to measure variations of forces exerted by layers of water just a single water molecule thick.

At 0.25 nanometer, a water molecule seems to be pretty darn small. How small? In other words, exactly what is a nanometer? You probably know it’s a billionth of a meter, or 10-9m=0.000000001 m, but that is of little help. How can we visualize such a small scale? Here is one way: Not to split hair, but if you actually were to split hair, you would need to split a hair to 100,000th of its width to make strands a nanometer thick. Here is another way to try to visualize how tiny a nanometer is: A healthy, young human can walk about 5 km in an hour (at a brisk pace). This is 2,500 times a rather tall human’s height. Proportionally, if we were to shrink this human to 1 nanometer height, the shrunken human should be able to walk 2,500 her height or 2,500 nanometers in one hour. How long would it take our nanometer sized human to walk a distance equivalent to the height of a normal sized human? Or, in other words, if we were only 1 nm tall, what kind of distance could we explore just walking around? Take a guess before reading on…. Here it is: Our rather tall, full-sized human has a height of 2 m (or about 6’ 7” in feet & inches) = 2 x 109 nm = 2,000,000,000 nanometers. It would take 2×109/2,500 = 8×105hours = 91 years (!!) for our nanometer-sized human to traverse the length of the full-sized human. And that’s walking 24/7 at a brisk pace for 91 years –a (long) lifetime. This means if we were only a nanometer tall and were walking day and night for 90 years, all we could explore would be a few feet of territory. We are unimaginably huge compared to a nanometer. If our the molecules in our body would move like we do, a molecule would need 90 years to get from our toes to our ears. Fortunately, molecules move much, much faster than that, otherwise we wouldn’t notice that somebody stepped on our toes until decades later!

If we are a billion times larger than a nanometer, what is a billion times larger than we are? The distance to nearest star? The distance to the Andromeda galaxy? Make a guess… Ok, let’s calculate it. At a height of 2 m for our model human, the distance we are looking for is 2 x 109 m = 2×106 km = 1.25 million miles. That’s five times the distance of the Earth to the Moon. That’s pretty far – although not as far as we may have thought. The universe is a huge place. Five times the distance to the moon is certainly something we can think about traversing – as a matter of fact, some Apollo astronauts must have come pretty close to this distance, if we include orbiting the moon. But they were going much faster than just a brisk walk.

So it seems that these are distances our human lives have reached: One billion times smaller and one billion times larger than we are. From the molecules we are made of to the largest distance we have travelled.