The risk of radiation induced harm from a chest X-ray or a CT scan is overestimated in the community. A CT scan of the chest carries radiation dose of 0.66 milliGray and the harmful dose is >100milliGray. Moreover, we are always exposed to natural cosmic radiations all the time. If someone is still worried, they can do a low dose CT scan.
The table below shows the amount of radiation each test produces and illustrates that all the X-rays and CT scans produce the radiation dose that is far lower than the harmful dose of >100 milliGray.
The 2nd figure shows the effective radiation of the various tests and how they compare with the natural background radiation that all of us are exposed to on a daily basis. 1 mSv is equal to 1 milliGray.
What can you do? Do not avoid a chest X-ray or a CT scan out of fear of harm from radiation. Yes, these should be avoided, but if it is necessary, or if it is going to help you assess your condition more accurately, you should feel safe to go for it. In a case where you need to undergo CT scan often, for example, patients who have a nodule which requires yearly monitoring for any increase in size, or those who have been treated for lung cancer and now following-up with an yearly CT scan to ensure cancer is not coming back, you can go for a low dose CT scan of the chest. Low dose CT scan carries 5 times lesser radiation exposure than the traditional CT scan although the radiation exposure from a traditional CT scan is also much lower than the dangerous level of exposure.