The potential for radon-induced lung cancer is a function of the amount of exposure (alpha particle hits), length of exposure (time), and smoking history. Prolonged exposure to low levels of radon is equally as dangerous as short exposure to high levels of radon. Because our bodies have no threshold for radon exposure, no level is considered safe. The only safe level of radon exposure is when there is no radon.
Below is a radon-related health risk chart from the US EPA.