Atoms are very small[citation needed]. Seeing individual atoms is impossible: They are smaller then the wavelength of light.
Ok, but is it possible to see an atom doing something?
Lots of chemical reactions glow, but none of them are bright enough to see single atoms... but what about nuclear reactions?
Heavy elements like uranium often decay by the emission of a helium nucleus. The alpha particle is ejected with around a picojoule of kinetic energy: just about enough to produce a visible flash.
I used a 37 kBq of americium from a smoke detector as a source of alpha particles. Other options are old radium paint or pieces of uranium ore with exposed mineralization.
My scintillator is a square of plastic that came out of a broken alpha probe. One side of it has a white coating of zinc sulfide, which glows when struck by high-energy particles. There's no power source: All the energy comes from the radiation itself.
A magnifying glass helps direct the light into the eye's pupil. This is important because each alpha particle only produce a couple thousand photons.
To see scintillation, put an alpha source within a few millimeters of the screen, and turn off the lights. Because the light is very faint, you must let your eyes adapt to perfect darkness for several minutes. After a while, you should be able to see a dim glow around the alpha source.
With magnification, this glow resolves into thousands of momentary points of light. To me, it looks like a roiling sea of sparks: each "spark" is light produced using the energy released by a single atom.
Experiment notes.
Full dark adaptation takes upwards of 20 minutes, but I'm usually able to see the glow after five.
It helps to use averted vision: Look to the side of the source to exploit the higher light sensitivity of the rod cells in peripheral regions of your retina. This same "look-at-it-but-don't-look-at-it" trick is very useful in astronomy.
With weaker sources the diffuse glow may not be visible: If you can't see it, go straight to the magnifying glass.
Alpha particles can only travel a few centimeters in air, and loose energy with every millimeter. The source must be close to the scintillation material for flashes to be visible.
A scintillation screen usually has just one side coated with zinc sulfide: only the matte side will glow when exposed to alpha particles.
This effect is impossible to film: The only way to see it is to do the experiment yourself.
If you don't want to mess around with three different things in a perfectly dark room, you can by a pre-assembled spinthariscope for around $60.