A method for the production of an adsorbent precipitated on a carrier, comprising a precipitation of an inorganic adsorbent capable of Cs + adsorption from liquid medium, on polymer based spherical activated carbon serving as the carrier, wherein a synthetic polymer is utilized for the production of the activated carbon, and wherein the activated carbon has - a total pore volume according to Gurvich of at least 0.5 cm 3 /g, wherein at least 50% of the total pore volume are embodied by micropores having a pore diameter of not more than 20 Å, - an average pore diameter of not more than 40 Å, and - a BET surface of at least 1,000 m 2 /g, the method comprising the following steps: a) providing the polymer based spherical activated carbon as a carrier, subsequently either b1) and c1) b1) impregnating the carrier with an aqueous solution, containing (i) hexacyanoferrate or hexacyanoferrate anions, and (ii) NH 4 +, Li +, Na +, K +, or Rb +, c1) adding to the impregnated carrier an aqueous solution of a salt of a bivalent, trivalent, or quadrivalent metal cation, by means of which the inorganic adsorbent precipitated on the carrier is retained in the form of a complex hexacyanoferrate or of a complex hexacyanoferrate, or b2) and c2) b2) impregnating the carrier with an aqueous solution of a salt of a bivalent, trivalent, or quadrivalent metal cation, c2) adding to the impregnated carrier an aqueous solution, containing (i) hexacyanoferrate or hexacyanoferrate anions, and (ii) NH 4 +, Li +, Na +, K +, or Rb +, by means of which the inorganic adsorbent precipitated on the carrier is retained in the form of a complex hexacyanoferrate or of a complex hexacyanoferrate, subsequently d) washing of the carrier comprising the precipitated adsorbent, and e) optionally drying of the washed carrier comprising the precipitated adsorbent. - a total pore volume according to Gurvich of at least 0.5 cm 3 /g, wherein at least 50% of the total pore volume are embodied by micropores having a pore diameter of not more than 20 Å, - an average pore diameter of not more than 40 Å, and - a BET surface of at least 1,000 m 2 /g, a) providing the polymer based spherical activated carbon as a carrier, subsequently either b1) and c1) b1) impregnating the carrier with an aqueous solution, containing (i) hexacyanoferrate or hexacyanoferrate anions, and (ii) NH 4 +, Li +, Na +, K +, or Rb +, c1) adding to the impregnated carrier an aqueous solution of a salt of a bivalent, trivalent, or quadrivalent metal cation, by means of which the inorganic adsorbent precipitated on the carrier is retained in the form of a complex hexacyanoferrate or of a complex hexacyanoferrate, or b2) and c2) b2) impregnating the carrier with an aqueous solution of a salt of a bivalent, trivalent, or quadrivalent metal cation, c2) adding to the impregnated carrier an aqueous solution, containing (i) hexacyanoferrate or hexacyanoferrate anions, and (ii) NH 4 +, Li +, Na +, K +, or Rb +, by means of which the inorganic adsorbent precipitated on the carrier is retained in the form of a complex hexacyanoferrate or of a complex hexacyanoferrate, subsequently b1) impregnating the carrier with an aqueous solution, containing (i) hexacyanoferrate or hexacyanoferrate anions, and (ii) NH 4 +, Li +, Na +, K +, or Rb +, (i) hexacyanoferrate or hexacyanoferrate anions, and (ii) NH 4 +, Li +, Na +, K +, or Rb +, c1) adding to the impregnated carrier an aqueous solution of a salt of a bivalent, trivalent, or quadrivalent metal cation, by means of which the inorganic adsorbent precipitated on the carrier is retained in the form of a complex hexacyanoferrate or of a complex hexacyanoferrate, or b2) and c2) b2) impregnating the carrier with an aqueous solution of a salt of a bivalent, trivalent, or quadrivalent metal cation, c2) adding to the impregnated carrier an aqueous solution, containing (i) hexacyanoferrate or hexacyanoferrate anions, and (ii) NH 4 +, Li +, Na +, K +, or Rb +, by means of which the inorganic adsorbent precipitated on the carrier is retained in the form of a complex hexacyanoferrate or of a complex hexacyanoferrate, subsequently (i) hexacyanoferrate or hexacyanoferrate anions, and (ii) NH 4 +, Li +, Na +, K +, or Rb +, d) washing of the carrier comprising the precipitated adsorbent, and e) optionally drying of the washed carrier comprising the precipitated adsorbent.