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Radon is a radioactive element which exists as a gas. Chemically it is described as 'noble' or 'inert' which means that its atoms as a whole do not readily react with other atoms. However radon atoms can 'decay' by undergoing nuclear fission to produce radioactive 'daughters'. 
 

Radon exists in many isotopic forms, the most important being radon-222. A much less common isotope, radon-220 is often called thoron.  Typically these arise from uranium bearing feldspars from some forms of pink granite of igneous origin but might arise in other circumstances as well. The gases decay to so-called "daughters" and it is these isotopes which release alpha particles in the lung. The national average radon activity in houses in the UK is 20 becquerels per cubic metre and this is associated with the life-time risk of lung cancer of 1 in 300. At the "action level" which is 10 times this national average (ie 200 becquerels per cubic metre), the life-time risk of lung cancer is similarly increased 10 fold (1 in 30). It is possible to measure exposures through appropriate dosemeters and to reduce the risk by adaptation of building techniques to prevent radon gas rising through the ground into the house. 

The animated image shows how uranium can generate radon gas by fission. The radon gas will itself undergo further fission to produce radioactive 'daughters'. The alpha particles produced by radon daughters are not powerful enough to penetrate the human body from outside it. However, if radon is inhaled, the alpha particles generated by the daughters can cause harm to cells in the lungs and elsewhere. This may result in an increased risk of cancer

While the above account relates primarily to radon, similar considerations apply to the almost identical radioactive gas thoron.

 
 

The animated image shows how radon gas diffusing out of the ground can be forced or sucked into homes thus resulting in much higher concentrations indoors than outdoors. The animation might give you some ideas as to how exposure in homes could be reduced. For example an impermeable membrane could be installed at floor level, fans could suck air containing radon from underneath the ground floor and expel it directly into the atmosphere, where it disperses.