Ignoring the deterrent factor, a single nuke isn't that bad in terms of radiation, it's only when there are multiple nukes in the same area that they become a problem
Compare Hiroshima to Bikini Atoll and you'll understand.
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In terms of radiation, everywhere within an 8km (max) radius will be irradiated. In terms of radiation that is pretty bad. Because radiation alters cells on a molecular level causing mutations. I am aware that the figures vary from each bomb but radiation is something that we dont want alot of on this planet from a biological standpoint. I am not totally against these weapons as of now unless they are used on a civilian population, or used too much. But i do believe that we would be much better off without them.
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Maybe I should've added "over time" Yes you'll get irradiated if your within a few miles of a nuke, but unless you're dropping several nukes in close proximity that damage will heal. I mean, nuke or missile, either way your dead - not much difference there - and over time there really isn't much difference to the surrounding environment either.