Gamma radiation may go forever, but intensity decreases exponentially as you get away from the source. And I'm pretty sure it can be distorted, blocked, etc.
Since there has to be some sort of radioactive stuff either on or inside those poor victims, I guess the police would be able to locate it.
Not necessarily. Exposure from the outside could kill you without the stuff ever actually touching you. (Think of Clark and kryptonite.)
And even if it's something injected... Radioactivity comes from unstable atoms. They're too big. All those protons stuck together in the nucleus repelling each other. The atom breaks apart, or shoots out pieces of itself. And each atom that sends out a piece of itself changes, becomes a different, smaller atom. Becoming more stable. And reducing the amount of the original substance.
Of course, the less of that substance you have, the less radioactive it is, and the slower it decays. So you don't say that it ever fully goes away. Instead, you have what's called a "half-life." It's the amount of time it takes for half of a given sample to decay into something else.
Let's say it's 12:00 and you have one pound of substance X, which has a half-life of one hour. At 1:00, you'd have half a pound of X and roughly half a pound of whatever X decays into (slightly less, since the radiation itself carries away some mass). At 2:00, you'd have half of that, or 1/4 of a pound. At 3:00, you'd only have 1/8 of a pound of X. And so on.
Now, something that highly radioactive would probably decay into some other (slightly less) radioactive substance, which would have its own, longer half life. That would, in turn, decay into something slightly less radioactive, and so on until, eventually, you ended up with something stable. Generally lead.
But... if you had something with a really short radioactive half-life, it would not only be highly radioactive (and thus quickly lethal), there might be only a tiny amount of it left by the time they found the bodies. Maybe not even enough to be detectable against normal background radiation.
Any material radioactive enough to kill quickly would burn the veins while being injected - this will definitely leave evidence an ME could find. It would also be excruciatingly painful for the victim.
Good point. That could really hamper the IV. Perhaps even damage the vein enough to cause internal bleeding.
But... There are ways around that. A slower drip. Splitting into multiple doses. Injection by syringe rather than intravenously (though you'd still get burns at the injection site). Surgical implantation.
Or other time release methods. For example... this could be tricky, but it might be possible to inject microbeads. Tiny samples of whatever you want to inject encased inside a protective coating, which gradually dissolves (or perhaps, in this case, burns away). Not sure what you'd use in this case, since heavy metals like lead are toxic in and of themselves. But it might be possible to find something that would work. Particularly given the advanced technology available in the L&C universe.
Still painful and all. Still leave burns. I mean, you are talking about injecting enough radioactive particles to kill someone from the inside out. But it might be less obvious from the outside, and it could get you around the problems of damaging the vein you're trying to inject into before you're done with the injection.
