K hc2p32

where 4>, the work function, is characteristic of each metal but usually in the range of a few electron volts (eV) [2]. The important thing was that the same value of h was obtained from this experiment as from the light spectrum analysis of Planck. It was found that the energy of the electrons (as distinct from their number) was not affected by the intensity of the light but only by its frequency. So it was clear that the light was coming in discrete chunks of energy, which were completely absorbed in releasing the electron from the metal (the binding energy of the electron to the metal is 0).

As far as electrical charge Q is concerned, the limit of smallness is the charge -e of the single electron, where e = 1.6 x 10"19 C. This is an exceedingly small value, so the granularity of electrical charge was not easily observed. For most purposes electrical charge can be considered to be a continuously distributed quantity, described by volume density p or surface density a.

The first measurement of the electron charge e was made by the American physicist Robert Millikan, who carefully observed [3] the fall of electrically charged microscopic droplets of oil in air under the influence of gravity and a static electric field. Following the application of Stokes' Law, (see equations 2.7 and 2.8) the velocity of fall in air is given by v = (mg+ neE)/(6 nv R), (3.3)

where n is the number of electron charges on the droplet. By making measurements of the electric field E needed to make the velocity v of a single drop come to zero, as its charge number n changed in his apparatus, Millikan was able to deduce the value of the electron charge e.

These historical developments, seminal and still highly relevant to the origins of nanophysics, are summarized in introductory sections of [6] and [7] which are quickly available and inexpensive.

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