When radon decay products are inhaled they stick to sensitive lung tissue. Being short-lived, they will break down while they are in the lungs. This exposes the lung tissue to radiation.
If the alpha particle hits the live pulmonary epithelium DNA, it can damage the cancer suppressant genes and increase risk for contracting lung cancer. In addition to the alpha particle causing double and single strand DNA breaks, the alpha particle can also cause ionization of material around the DNA that can also damage it (shown on right of DNA strand).
This is the mechanism that radon (and more specifically the radon decay products) can lead to an increased risk of lung cancer.
Smokers who are exposed to radon are at a higher risk of developing lung cancer. 62 of every 1000 smokers who are exposed to radon will die from lung cancer. Smoking 1 1/2 packs of cigarettes per day has the equivalent radiation dose as from 300 chest x-rays per year (National Institutes of Health).
Why Does Smoking Intensify Radon Exposure?
Polonium-210 is a radioactive element found in cigarettes. When it gets into the lung, it causes damage the lung similar to radon. There is a 20 times greater chance of dying from lung cancer if you are a smoker (World Health Organization).