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A vacuum is a region of space with nothing in it, so when an experiment is done in a vacuum, all the photons, air, and particles are removed from the region to create a space of nothing but pressure. The photoelectric experiment showed this effect of electrons being "ejected" from the metal.
I believe the purpose of a vacuum in this experiment ensures that the ejection of the electrons from the metal observed was a result of the applied photons, and not other variables that could have potentially contributed to the ejection of the electrons if not removed (i.e. air molecules).
I believe when Dr. Lavelle stated that the photoelectric effect must be done in a vacuum, this means that the experiment must be conducted free of any external particles. There must be nothing in the region in which the experiment takes place, simply whatever pressure may exist (but free of any protons, electrons, etc.)
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