polonium-210

I have my doubts as to who, if anyone, poisoned with polonium-210 the russian ex spy Alexander Litvinenko.   Although at first, I thought that the whole "Putin killed him" was a strong possibility, I now have my doubts.  
The reasons for that are three.  The first is that it does not make any sense to use something as "exotic" as radiation poisoning, to execute someone.  There are plenty of poisons available that leave far less traces than...radiation.  
The second is that Traces of radiation were found, and continue to be found in many places all around Europe.  If Alexander Litvinenko was poisoned shortly before dying, even a couple of days, there was no way for him to spread the radiation by visiting all these places around Europe in such a short time.
The third reason is one that when I think of the first two with it, brings some interesting possibilities to the table of conspiracies.  This man recently turned into follower of Islam.  By itself it might not mean much, but considering the problems with the previous theories, it makes another theory available. What if, this guy was smuggling in radioactive materials to support an attack in the UK?  From what I understand Polonium 210 is not the best material to make a nuke, but it should be good enough to make a so called, dirty bomb.  At some point there was a leakage, Alexander was trying to cover his own tracks to perhaps save his accomplices from exposure, and knowing he was going to die anyhow, accused Putin in his effort to confuse the invistigators looking for answers.  He knew that sooner or later the real material for his ill health would be found so if he has accused Putin before they figured it out, it will all look "normal".
The media don't seem to mention too much his recent change of religion, perhaps trying to be pc, or just not thinking about it in the same way as I.  
I hope that investigators will do a good job, because I am worried that perhaps there is a real plan to attack the UK (or perhaps even Russia) with a dirty bomb.