Dual Nature of Radiation and MatterIntroduction

By the end of the nineteenth century, Maxwell's equations and Hertz's experiments of 1887 had made the case for the wave nature of light look complete. At the same time, experiments on electric discharge through gases at low pressure led to a string of discoveries: X-rays (Roentgen, 1895) and the electron (J. J. Thomson, 1897). At a pressure of about 0.001 mm of mercury, a discharge passes between the two electrodes of a tube, and the glass opposite the cathode glows, yellowish-green for soda glass. The glow is caused by radiation that seems to come from the cathode: cathode rays, discovered by William Crookes in 1870. In 1879 he suggested that they were streams of fast, negatively charged particles.

J. J. Thomson confirmed this. He sent the rays between charged plates and through a magnetic field at right angles to the electric field, and was the first to measure their speed and their specific charge e/m. Below, B = 1.0 mT points into the page. The electric force eE pulls each electron up, towards the + plate, and the magnetic force evB pushes it down.

With the beam going straight, the two forces balance: eE = evB, so v = E/B = (4.0 × 10⁴ V/m) ÷ (1.0 × 10⁻³ T) = 4.0 × 10⁷ m/s, about times the speed of light. Thomson found speeds of 0.1 to 0.2 times the speed of light (3 × 10⁸ m/s). Switching E off and measuring how sharply B alone bends the beam then gives e/m; the accepted value today is 1.76 × 10¹¹ C/kg. It is the same whatever metal the cathode is made of and whatever gas is in the tube, so the cathode-ray particles are universal.

Packets of Charge

Around 1887 it was found that some metals give out slow, negatively charged particles when ultraviolet light falls on them, and that hot metals do the same. Their e/m turned out to be the same as that of cathode rays: particles produced in very different ways were identical. In 1897 Thomson named them electrons and suggested that they are fundamental, universal constituents of matter; he received the Nobel Prize in Physics in 1906.

In 1913 R. A. Millikan measured the charge on tiny charged oil droplets, one at a time. Here are the charges he might find on six drops. Slide the unit u until every drop sits on a line at a whole number of u. Find the largest unit that works.

u = ${u} × 10⁻¹⁹ C

Every drop carries a whole number of elementary charges, e = 1.602 × 10⁻¹⁹ C: electric charge is quantised. Knowing e and e/m gives the mass of the electron: m = e ÷ (e/m) = (1.602 × 10⁻¹⁹ C) ÷ (1.76 × 10¹¹ C/kg) = × 10⁻³¹ kg.