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I know matter and antimatter annihilation release a lot of gamma rays which are considered ionizing radiation if I am not mistaken. But what if the explosion happened on the surface of the earth, would the the material taken into the fireball cause fallout afterwards ?

My question in another form, what causes fallout ? and is ionizing radiation capable of radiating materials for a long time ?

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Actually I see now relation between these questions and mine. They don't include the radiation part I need to know in this question. –  Abanob Ebrahim Aug 12 '13 at 0:52
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In a fission bomb, the fallout consists of fission-decay fragments, which are nuclei that can have long enough half-lives to be transported by winds. Fusion bombs are basically the same idea, because they use fission triggers.

and is ionizing radiation capable of radiating materials for a long time ?

In theory, yes, e.g., exposure to neutrons in reactors can be used to intentionally produce radioactive isotopes. In practice, although nuclear bombs must produce this kind of artificial transmuation of the surrounding matter (e.g., they do emit neutrons), I think there isn't enough of this kind of process to contribute noticeably to the fallout.

Matter-antimatter annihilation from a hypothetical macroscopic explosion would produce the same particles as proton-antiproton annihilation in microscopic quantities in accelerator experiments. You get high-energy (~100 MeV) gammas, medium-energy (e.g., 511 keV) gammas, pions, muons, and neutrinos. The neutrinos fly off harmlessly and undetectably into outer space. Matter is nearly transparent to the high-energy gammas; the downward-emitted ones are absorbed somewhere underground. The medium-energy gammas are absorbed in nearby matter. The pions and muons are unstable and decay quickly into stable particles such as electrons. Nothing long-lived is produced.

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So since there is no fission-decay fragments in the annihilation process then there won't be fallout ? In another way, say a hypothetical antimatter bomb exploded and there was a building that survived the blast and the heat but was subjected to a lot of gamma radiation, so is it safe to be around this building say after a week from the explosion ? –  Abanob Ebrahim Aug 12 '13 at 0:59
@AbanobEbrahim: Yes. –  Ben Crowell Aug 12 '13 at 1:00
@BenCrowell Wouldn't photonuclear reactions cause induced radiation? Heavy elements (tungsten and above) would emit alot of garbage on 100MeV and cause radioactivity fallout. –  BarsMonster Aug 12 '13 at 1:08
@BarsMonster: I could be wrong -- my intuition is based on experience with 1 MeV gammas, not 100 MeV -- but I think the cross-section for processes like gammas directly knocking out protons would be orders of magnitude lower than the cross-section for the dominant interactions with matter, such as e+e- pair production. –  Ben Crowell Aug 12 '13 at 1:31
High energy gamma can create radioisotopes in a number of ways, but as Ben suggests these events are a very small fraction of interactions. Maybe you could measure the effect, but you shouldn't have to worry about health effects related to the dose. –  dmckee Aug 12 '13 at 7:11
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Antiproton proton annihilation is a strong interaction. It will last on the order of 10^-23 seconds. That would create a blast of energy but those atmospheric processes take order of milliseconds. Even if they take order of microseconds all the decays will have happened before any material enters the blast.

Anyway how much energy will be in the blast and how much will be radiated to space in the 2pi sphere pointing out to space before leaving much of the energy in the atmosphere is a matter of detailed modeling. It might be quite possible that the energy will dissipate as 1/r^2 into the ground without managing to heat up the atmosphere enough to create a blast. So it could be just a sterilizing wave, killing live things in its direct path; note 1/r^2 is strongly dissipative 1000 meters away the effect goes down by 10^6. This applies also to any radioactivity from decay product interactions with the ground.

All this is a matter of detailed modeling but nobody will do it for you since it is impossible to create such a situation anyway. You should pick up a more realistic project.

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Why do we even need material to enter the blast ?! and are you trying to say that the annihilation of matter and antimatter will NOT look like or have similar effects as nuclear weapons ?! Well, you are the first person to say so. But also keep in mind that the nuclear chain reaction is so fast too, and still it makes a huge explosion. –  Abanob Ebrahim Aug 12 '13 at 12:07
Also, what happens in nuclear fission or fusion that is so different ? I mean on which form is the energy released ? There is also a partition of the mass lost, which is the source of energy just the same as antimatter. One last thing, if the annihilation releases gamma rays, if I am not mistaken, gamma rays traveling in air heat it up and thus creating the fireball. I might be wrong though, so tell me what you think. –  Abanob Ebrahim Aug 12 '13 at 12:49
@AbanobEbrahim I have stated in other answers that the difference between fission fusion and annihilation as you visualize it lies in the energy of the products. To get an explosion blast you have to heat the air fast enough to transfer energy to the individual atoms which then heat up very fast the gas, the heat produces fast atmospheric changes and the blast happens. The products from the annihilation have individual energies of the pions and gammas hundreds of times higher than of atomic or hydrogen bombs. –  anna v Aug 12 '13 at 13:16
This means that in the air they will mostly see empty space, since the higher the energy the smaller the wavelength, and it is quite probable they will go through to the ground or outer space without interacting much. They will not get the chance to transfer energy to the air molecules to heat them. –  anna v Aug 12 '13 at 13:18
I am saying that the models used for estimating the effects of an Hbomb are not good enough for a hypothetical annihilation bomb. One would have to take into account all of the above in the model to simulate what will happen under given boundary conditions, but certainly the studies for fission and fusion explosions are not adequate. –  anna v Aug 12 '13 at 13:25
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