KREEP
The lunar geochemical component KREEP contains trace amounts of the radioactive elements Thorium and Uranium. Regolith dust formed from this rock is a serious health hazard.
The radiation given off is Alpha particles (helium nuclei) and they do not penetrate very effectively. The direct radiation is stopped by any pressure vessel wall and even a well designed layer of spacesuit material.
The problem is that if the dust is ingested into the human body, the particles will lay directly on lung or intestine tissue and are carcinogenic. Ingestion of the dust must therefore be rigorously limited.KREEP is concentrated in the Oceanus Procellarum (Ocean of Storms) and Mare Imbrium (Sea of Rains) with a major concentration south of Crater Copernicus. This region covers about 40% of the Earth-facing side of the Moon. Based on the small number of lunar samples returned, low KREEP regions measure 8% or less of the radioactive elements in their dust compared to the high KREEP regions. With current technology, the entire high KREEP region is not acceptable for any long-term human settlement or manned mining operation.
The high KREEP region contains many sites of interest to science, particularly those of volcanic origin. Even short scientific expeditions there will require special procedures to prevent ingestion of dust and the removal of dust from all returning equipment.
Radon Gas
Another source of dangerous radiation is the radon gas that is created in the decay of trace amounts of uranium found naturally in lunar rocks. This gas is very heavy and concentrates in low areas. This type of radiation is easily stopped by even a thin layer of material, but radon is carcinogenic if ingested directly into the body.
Even though sensitive scientific equipment has been able to detect radon on Luna, the quantity of radon gas is such that it can be ignored. The lunar atmosphere is so thin that the most massive component, Argon, is present in only 30,000 particles per cubic centimeter, that is 2 trillionths of a gram per cubic meter. Radon is so scarce that it is not even mentioned in the list of components in the lunar atmosphere article. See the Moon Fact Sheet from NASA.
Radon has also been detected from lunar outgassing events.
http://lunarpedia.org/index.php?title=Radiation_Problem