The Structure of the Atom 163
determine the absolute value of the charge it was carrying. He found that
the charge on the oil drops came in discreet units, which he labeled e.
This unit, e, is the absolute charge of the electron and is a fundamental
constant of nature. It is an extremely small number equal to 1.6 × 10-19
coulombs. A coulomb is the amount of charge that flows through a
standard 100-watt light bulb in approximately one second. The smallest
charge observed for an oil drop was –e. The charges on the other oil
drops were always equal to an integer times e. Thus, one observed oil
drops with charge +e, –e, +17e, –10e, +3e, etc., but never with charges
like 0.5e, –1.1e or –2.37e. Millikan concluded that an electron carries the
charge –e and that the charge on his oil drops was due to an excess or
lack of a given number of electrons. The oil drop with charge +17e was
missing 17 electrons whereas the oil drop with charge –10e had 10 extra
electrons.
Once the charge of the electron was known, one was able to
determine the mass of the electron using Thomson’s determination of
the charge to mass ratio. One discovers, in this way, that the electron
is an enormously small object with a mass of only 9.1 × 10-28 grams.
Exploiting Thomson’s determination of the charge to mass ratio of
the hydrogen ion, H+, and assuming that it has the charge +e, we
find that the mass of the hydrogen atom is 1.66 × 10-24 grams or almost
2000 times the mass of the electron. Once the mass of the hydrogen
atom is determined, the absolute masses of all the other atoms are
determined also since the relative mass of the atoms is known from the
work of the chemists of the first half of the nineteenth century. The
oxygen atom is approximately 16 times the mass of the hydrogen
atom and the carbon atom is 12 times the mass of the hydrogen atom.
From the absolute weights of the atoms, we can determine the number of
hydrogen, carbon or oxygen atoms in one gram of hydrogen, 12 grams of
carbon or 16 grams of oxygen, respectively. This number, which is called
Avogadro’s number, is equal to 6 × 10^23. Making use of our knowledge
of the density of graphite, which is pure carbon, we can determine the
volume occupied by a carbon atom and, hence, its radius, which turns out
to be approximately 10-8 cm.
Actually, Avogadro’s number was not originally determined by
Millikan’s experiment of 1909 but by Einstein’s analysis of Brownian
motion in 1905. Brownian motion, first observed in 1827 by the botanist
Robert Brown, is the observed erratic, jerky motion of microscopic
pollen grains suspended in water. The smaller the pollen grain, the more