Orders of Magnitude

The very small and the very large ...

The atom, and the nucleus in particular, belong to the world of the infinitely small; a world whose minuscule size is almost impossible to grasp. The units and orders of magnitude we use in our everyday lives no longer have any sense, and so the numbers being used, whether large or small, quickly become too extreme for us to properly understand. Here are a few helpful points:

Nesting Russian dolls
There are fifteen orders of magnitude separating the scale of our daily lives from that of nuclear matter – nuclei, nucleons and quarks – the playing field of radioactive phenomena. The living matter of a tree, which can reach 20 or 30 metres into the air, is comprised of cells containing large molecules formed of minuscule atoms with a radius of several billionths of a metre. As small as they may be, atoms are some 100,000 times larger than the nucleons which agglomerate to form the subatomic nuclei. The Russian doll process has not yet finished: nuclei are in their turn made up of quarks.

Dimensions: The radii of atoms are of the order of tenths of billionths of a metre. The length of a chain of a billion atoms would barely pass the 20cm mark. A proton is a hundred thousand times smaller, and the length of the same proton chain would only be 2 microns: two thousandths of a millimeter. Nuclei are somewhat bigger, but not by much.

Speeds: Nothing travels faster than the speed of light in vacuo. It takes light 8 minutes to reach us from the Sun, at a speed of 299,792,458 km/s. The atom’s electrons are nowhere near as fast, but their velocity is still of the order of several thousand kilometers per second.

Time scales: It takes light a fraction of a billionth of a billionth of a second to pass through a tiny atom. This minuscule length of time can be treated as the tick-tock of a pendulum working at the rhythm of the atom: a length of time far smaller than the second. In one second, an energetic electron with a speed of 3,000 km/s – one hundredth of the speed of light – can make as many orbits of the atom as there will be heartbeats on Earth over the coming decade.

Energies: In absolute terms, these tiny particles have infinitesimal energies. But the speeds reached can be very high – out of all proportion to the energies provided by the thermal agitation of the atoms and molecules. An alpha particle with an energy of 4 million electronvolts or MeV, for instance, can be ejected at a speed of 15,000 kilometres per second. Once it slows down and completes the transformation into a helium nucleus, the speed drops to a few kilometers per second and the energy becomes that of most gaseous molecules: a few electronvolts.

When the numbers of nuclei involved become high, the energies released in a nuclear process may turn out to be enormous. Such reactions occur naturally in the stars. In nuclear reactors, fission chain reactions of uranium 235 liberate energies far greater than those released by regular fuels. The energy liberated by the fission of an uranium nucleus is of 200 million electronvolts, 33 million times greater than the energy liberated by the combustion of a carbon atom.

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