Small distances

In the last post, I looked at how far we can see. This time, lets try the opposite, what is the smallest length we can think of. Lets start with that well used yardstick, the human hair. As a person grows up, their hair gets stronger and thicker. An adult’s hair is between 17 to 181um (micrometers) thick. That is 0.017 to 0.181mm thick.


A human hair seen through an electron microscope

Our ability to see small things greatly increased in the 17th century with the coming of the microscope. This led to a slew of discoveries. In 1665, Robert Hooke published a book titled Micrographia where he illustrated some of the things he had observed in his microscope.


Robert Hooke’s microscope

Hooke’s drawings of a louse and a flea from Micrographia

But there are limits to such optical microscopes. In practice, the lowest value of resolution is about 200nm (1nm = 0.000001mm). But no fear, we can go further.

In 1925, the French aristocrat scientist Louis De Broglie proposed that particles like light, also had a wavelength. This wavelength would be inversely proportional to their momentum. This was confirmed in 1929 and led to the interesting idea that if particles could behave like light, maybe they could be used for things that light was used for, like building microscopes.


Louis De Broglie

This was how the electron microscope was born in 1931. The electron microscope works on the same principle as an optical microscope but uses electrons instead of light and electro magnets instead of lenses to focus the electrons. A beam of high energy electrons are fired at the target to be magnified. Some electrons pass through while others are reflected. These passing electrons can then be magnified using electromagnets and viewed on a fluorescent screen.


Electron microscope

A bacterium and an ant viewed through an electron microscope

More recently, microscopes using quantum effects have been developed. One is the Scanning Tunnelling Microscope. Since electrons behave like waves, they can leak past barriers. This is called tunnelling. The number of electrons that leak across a barrier depends on the thickness of the barrier.

In a scanning tunnelling microscope, a sharp metallic needle point of the thickness of a single atom moves slowly across the surface of the target at a distance of an atom’s diameter. Electrons tunnel from this tip across the target to the base on which the target is placed. By measuring the very small current between the needle and the base, the thickness of the target is measured by noting the changes in this current.


STM image of Cobalt atoms arranged in an ellipse

Another method being used is called photoionization where atoms are excited using a laser and start emitting electrons. These electrons are drawn to a detector. The distribution of current in different parts of the detector is used to reconstruct an image of the atom.


Image of a hydrogen atom obtained through photoionization

Now a hydrogen atom is about 1.2*10-10m in diameter. The proton that forms the tiny nucleus of the atom is only 10-15m in diameter.

Finally, physicists talk about one more length, called Planck’s length which is about 10-20 times smaller than the diameter of a proton or 1.6*10-35m. This is the smallest length conceived of yet. At this level the effects of quantum mechanics collide with the effects of gravity and our theories of physics become very uncertain.

Can there be particles smaller than Planck’s length? Well, there are some people thinking about what that would mean. If such things exist, they may not even be matter any more.




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