Can Radioactive Particles Be Filtered Out of Water?

I think disposing of filters contaminated with radioactive elements would pose a bigger problem than filtration.

http://www.godlikeproductions.com/forum1/message1418906/pg3

We have to figure out the earth too. I heard there was some rock, I believe it began with a "Z" that they used to clean up Chernobyl soil.

http://www.filtsep.com/view/722/filtration-in-nuclear-power/

Reverse osmosis with ion exchange resins. I wonder if that will fit under my sink.... Seriously, NO. There is always something left over to dump into our food chain.
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Water filtration
Power plants have conventional and unique water filtration requirements. The make up water for the steam generation system is identical to fossil power plants. Pre-treatment is followed by reverse osmosis systems. Filters for the cooling tower system and filters for plant drinking water would also be conventional. The steam turbine requires conventional lube oil filers. Filters are required to purify the condensate. Ion exchange resins are also utilised.
Dow just announced that its DOWEX™ MONOSPHERE™ ion exchange resins 650C and 550A for condensate polishing, along with DOWEX™ MARATHON™ C, DOWEX™ MARATHON™ A and DOWEX™ MARATHON™ WBA series for brine cleaning will be installed at Ling Ao Nuclear Power Plant (Phase II), which is located adjacent to the Daya Bay Nuclear Power Plant, and together comprise one of the largest, total installed capacity nuclear power bases in China.
The deep-bed condensate polishing systems in pressurised water reactor (PWR) nuclear power plants filter corrosion products transported from the main condenser to help control secondary cycle steam generator chemistry. It requires complete separation of the mixed resin to improve effluent water quality. Excellent mechanical strength and oxidative stability are also desirable features for less release of high megawatt (MW) > 1000 total organic carbon (TOC) species from cation resin to help minimise downstream sulfate excursions.
There are a number of special applications as well. They include the fuel pool, radwaste, reactor water cleanup, protection for radioactive exposure in the steam system, and removal of irradiated particulate in the reactor cooling pump.
Pall recommends its Ultipor GF Plus filters to optimise the visual clarity in the fuel pool. Pall radwaste filtration systems provide decontamination of liquid radwaste. Complete backwashable systems provide continuous automated service for small- and large-flow applications. Disposable systems are equipped with filter elements that are highly permeable, sturdy and efficient.
For reactor water cleanup (RWCU), Pall offers PMM septa and Rigimesh septa as alternatives to spiral welded mesh, wedge wire, and coarse metal elements commonly found in RWCU systems.
In addition to replacement activity there is some upgrade activity of the older plants. For example the WE Energies Point Beach nuclear plant has been operating since 1970.
The original water treatment design consisted of intake screens; lime-softening solids contact clarifier, one multimedia filter, two cation exchangers, one vacuum deaerator, two anion exchangers, and a polishing mixed-bed demineraliser.
In 1999, water treatment system improvements were made with the addition of three 100-gpm reverse osmosis (RO) units. The organic traps were converted to cation resin softeners and the RO units were installed at the effluent of the softeners. The purpose of these changes was to reduce the level of organic compounds reaching the steam generators.
The RO systems are spiral-wound, five-stage units that operate at 75 percent recovery employing low pressure Dow FILMTEC LE-440i membranes.
In 2004, Point Beach installed a Memcor® microfiltration system to replace the chemical feed, clarifiers and multimedia filters. The microfiltration system employs PVDF membranes with a 0.1 micron rating. By eliminating the chemical feeds, the clarifier, and the multimedia filters, the unadulterated backwash wastewater from the membrane filtration system is routinely discharged directly back to Lake Michigan.
Membrane filtration has greatly improved the water quality at Point Beach Nuclear Power Plant. The plant has significantly reduced its operating costs, increased the reliability of the water treatment plant, and reduced the waste associated with the water treatment system."