After just 28 electrons, no regular pattern appears. a After 1 000 electrons, a pattern of fringes begins to appear. After 10 000 electrons, the pattern looks very much like the many-electron result shown in d. Two-slit electron pattern (many-electron result) Figure 39.22 (a)–(c) Computer- simulated interference patterns for a small number of electrons incident on a double slit. (d) Computer simulation of a double-slit interference pattern produced by many electrons.

You are working as a demonstration assistant for a physics professor. She wants to demonstrate to her students the buildup of the interference pattern for single electrons passing through a double slit, as shown. Her source of electrons will be a certain vacuum tube, in which electrons evaporate from a hot cathode at a slow, steady rate and accelerate from rest through a potential difference of 45.0 V. After being accelerated, they travel through a fieldfree and evacuated region before they pass through the double slits and fall on a screen to produce an interference pattern. To ensure that only one electron at a time is passing through the slits, she wants the electrons to be separated in space by d = 1.00 cm (perpendicular to the barrier containing the slits) as they approach the slit. She asks you to
determine the maximum value for the beam current that will assure that only one electron at a time passes through the slits.