nuclear-engineeringradiation
How radiation from Chernobyl disaster compares to cosmic radiation on the surface of the Moon (effect on human cells and electronic devices)?
Why Chernobyl liquidators suffered heavily from radiation, when on the Moon people and electronic devices were not affected?
Why could they not have a 30 meter pit below a reactor filled with water with a trap door holding the reactor up?
If you read about the Molten-Salt Reactor, you will find that it has something rather similar to this. In the image below, item number 13 is a freeze valve. If the reactor overheats, the plug melts and the molten core flows down to the tanks 10 and 11. This "escape route" would probably be passively cooled by something like atmospheric convection. Of course, this was just one design and we can't speak for all systems that might be used.
In the generation of reactors being built today, AREVA has implemented something called a "core catcher". It is basically a passively cooled sheet of metal at the bottom of the containment building that a molten core would fall on, and then be safely contained and cooled.
My latter example, however, is only a worst-case scenario because if at all possible, we would prefer to not harm the physical integrity of the fuel. The rods of present-generation nuclear fuel hold in radioactive gases at a pressure significantly above sea-level atmosphere pressure. If many of the rods break, then that is still a core failure, and will release lots of radioactivity. Because of our reliance on the physical integrity of a small thickness of heavily irradiated metal cladding, we really can't move it except under controlled conditions and very slowly.
On the surface of the Moon, the main source of radiation is energetic solar particles (mostly protons and electrons) and galactic cosmic rays (GCR). (The GCRs come out of the Solar system.) The gamma radiation (as a primary particle) is negligible. (The gamma flux in the space is very low...)
According to this article, most of the particle showers won't penetrate more than 0.5 m of lunar soil (with a density of 1.4 g/cm$^3$). (According to this presentation, the density of lunar soil ranges from about 1 g/cm$^3$ to 2 g/cm$^3$.) The showers have a sharp peak in the [energy deposit - penetration depth] relationship. After which the energy deposition usually drops to less than 10% of the peak value. (Only lightly ionizing particles remain.)
Although they couldn't study the contribution of neutrons (created in the particle showers), which can penetrate more rock than the charged secondary particles. (On current spacecrafts, 30-60% of the total equivalent dose might come from neutrons.)
Based on the article, about 0.5-1 m of soil might be sufficient.
Although the radiation level will be still higher than on the surface of Earth, it is hard to tell more without experiments or simulations. The problem is with the neutrons (and high energy muons). For these, the energy loss is not continuous, but characterized by discrete events. Thus they can often penetrate more material than expected by continuous energy deposit approximation. Thus also non-trivial if '8 km' of air can be substituted by 4 m of rock (as suggested by @CuriousOne). (Also partly because of the different composition of rock and air.)
Best Answer
The radiation in space has a different character than the radiation in Chernobyl after the disaster.
In Chernobyl, the most dangerous radiation was gamma and neutron radiation from the radioactive fuel, gamma from the materials around (in the first days mainly Tellurium 132 and Caesium 134, 137) and (mainly in the first few days) beta radiation from Iodine 131 from dust inhaled or food ingested.
In space, the prevalent concern is due to protons and other heavy particles (nuclei of helium and others).
There are ways to compare numerically effect of these different radiations on a person, for example by comparing absorbed dose per hour. However, absorbed dose quantifies only heat effects of the radiation. It is only a rough indication of subsequent long-term biological effects of radiation (cancer, leukaemia).
For this reason, RBE factor was introduced which gives an indication of how much worse the radiation is than gamma radiation, for the same absorbed dose. Taking this into account, the effective dose is given in rems or sierverts. However, this factor is not well understood for cosmic radiation and can be different for different organs.
It is hard to find reliable numbers on dose rates for the Moon environment and for Chernobyl the numbers vary greatly depending on where the person was present.
I found some information on estimated total dose for the Apollo astronauts. According to https://www.nature.com/articles/srep29901, which references
Bailey, J. Radiation protection and instrumentation. 105–113 (US Governement Printing Office, Washington D.C., 1975)
Assuming RBE=1 (that is a big if), this would be equivalent absorbed dose around 6 mSv.
According to https://www.oecd-nea.org/rp/chernobyl/c04.html, section "The liquidators",
For the subsequent cleanup operations, the above documents says
Thus the Apollo astronauts received much less effective dose than the average for the Chernobyl's liquidators. It seems like the radiation dose due to few day trip outside Earth's protection, including a short stay on the Moon surface, is not too dangerous. Of course, this depends on time of flight, as the cosmic radiation can get significantly more intense in periods of solar activity. Also on Moon's surface there may be areas more radioactive than the ones American astronauts visited.