Seriously though - don't x-ray yourself with sticky-tape. You can, and we'll tell you how. But seriously gang, don't.
First of all, let's demystify x-rays. An x-ray is, in many ways, not any different from visible light. Both are produced when electrons shake off a little of their extra energy. Sometimes that happens when they are pumped full of energy and temporarily jump to a higher energy level, only to jump down a bit later. Sometimes it happens when something snatches a lower electron off and atom and the higher electron gets taken down a peg or two. Occasionally it happens when an electron is zooming along and is pulled in a new direction by a nearby atom. The change in its direction causes it to lose energy.
In every case, the energy is emitted in the form of a photon. Photons have an energy level that corresponds to how much energy the electron dropped. Photons can only be absorbed by atoms that can absorb their particular energy level. Visible light photons can be absorbed (and re-emitted) by everything that we can see.
X-rays have such high energy that they pass through much of what we can see. Anything on the extreme low end of the periodic table of elements is of no use to an x-ray photon. Only bigger atoms have what it takes to absorb an x-ray. This includes metals and, of course, our bones. So that's it. An x-ray is just a photon with such high energy that it doesn't interact with any small-time atoms.
Why are any photons coming off scotch tape? Because when a section of tape is ripped off the roll, it glows. Why does it glow? Because it is triboluminescent. What's does it mean to be triboluminscent? It means that an object will glow when rubbed, crushed or ripped apart.
You can go around in that particular circle for a while. I did.
Basically, the idea is that electrons gravitate to one part of the tape when it's all bound together on a roll. If a section of tape is ripped off suddenly, the electrons are stranded and jump from one side to another. This jump emits photons, some visible light, and some x-ray.
Now, how to save on medical costs by performing unregulated, unsupervised, and possible dangerous experienced on your own, presumably injured, body parts. First of all, you need to get rid of that stupid air. Air ruins everything. If you were to unpeel some tape in a dark room filled with air, you would only be able to see the tape glow in short bursts - possibly in Morse code telling you what a total loser you were for needing oxygen.
So you have to construct a vacuum chamber. Put some sticky-tape and an automatic peeler in one end, some x-ray film in the other, and jam that broken limb in between. Then peel. The x-ray will take a little longer than the usual one third of a second. Since the x-rays are emitted in short bursts, it will take a whole second to x-ray your broken foot in your home-made x-ray machine. But hey, you constructed a vacuum chamber. Clearly, you have time.
After that, it's only a matter of taking your home-made x-ray and hobbling down to the nearest emergency room with a really, really smug look on your face.
You sure showed them.