Originally Posted by Akula2ssn
As a rule of thumb, probably in space. However, the term radiation is a very broad term covering many different forms from different sources. Different types of radiation can require different types of shielding. Some forms at some levels, the dead outer layer of your skin is sufficient. Some require use of lead or some metal for protection. Some can actually be made worse by metal shielding (ie Bremsstrahlung effect) thus a dense plastic is the preferred choice. Part of the reason we aren't directly bombarded by cosmic rays is because of the Earth's atmosphere. I think you can actually see a measurable increase in exposure to cosmic rays in people who fly at high altitudes regularly though I'd have to check on that. Another thing that has probably helped us here on Earth is our magnetosphere. I don't think Mars even has a magnetic field anymore. We aren't even sure if it ever had plate tectonic activity. While we do see what appear to be signs of it, overall, the planet is relatively featureless, suggesting that if it did have tectonics it ceased a long time ago and many of the signs probably have since been erased due to weathering over time. On top of that I believe Mars has less mass than Earth so less gravity and likely less atmosphere so there's potential of less protection planetside.
Sources of radiation are just as variable and are all around us. Lead 210 is one source of radiation that we are constantly exposed to here on Earth. It's naturally in the air and soil.
Radiation comes in essentially 3 different varieties.
and Gamma Radiation.
Alpha radiation is extremely weak and can be blocked by a sheet of paper. The radiation from the aftermath of of the Nagasaki and Hiroshima detonations is this type. It last a very very long time but it's extremely weak.
Beta Radiation, is stronger than alpha and weaker than gamma radiation. Usually another type of radioactive decay from isotopes. It's penetration is more powerful and can be stopped by a few millimeters of aluminum. This is the type of radiation coming from the sun on average. Highly charged and blocked by Ozone and the Earth's shields.
Gamma Radiation is a higher frequency form of the above. In a nuclearly detonation this is part of the initial flash point, or in super nova's it is the first sign (other than neutrinos) of an explosion. They are short lived but their high frequency allows them to penetrate just about the most densest material.
The sun can put out GRB's in CME's (coronal mass ejections) but this is not common and it's a direction blast so spacecraft have to be within the line of sight of the burst.