Measurement of Very Small Distances

The astronomical techniques of the previous sections work for very large distances, but at the opposite end of the scale — measuring the size of atoms and molecules — conventional length-measuring instruments like a Vernier calliper or a screw gauge are hopelessly inadequate; their least counts (typically hundredths of a millimetre) are enormously larger than an atom's size (of order $10^{-10}\ \text{m}$). To measure such tiny distances, physicists instead use an electron microscope or a tunnelling electron microscope.

The basic reason ordinary light microscopes cannot resolve atomic-scale features is that the wavelength of the light used to 'see' an object must be smaller than the object itself: visible light has a wavelength roughly in the range $4000\ \text{Å}$ to $7000\ \text{Å}$ (angstrom), so an ordinary optical microscope can resolve sizes down to only about $4000\ \text{Å}$. To measure smaller sizes still, a probe with an even smaller wavelength is needed — and as later studied in Class XII, every material particle (such as an electron) has an associated wave, whose wavelength can be made far smaller than that of visible light by accelerating the electrons appropriately. In a typical electron microscope, the electrons' wavelength is about $0.6\ \text{Å}$, which allows resolving atomic-scale sizes of order $1\ \text{Å}$. …