in chemistry, the steady decrease in the size of the atoms and ions of the rare-earth elements (rare-earth element) with increasing atomic number from lanthanum (atomic number 57) through lutetium (atomic number 71). For each consecutive atom the nuclear charge is more positive by one unit, accompanied by a corresponding increase in the number of electrons present in the 4f orbitals surrounding the nucleus. The 4f electrons very imperfectly shield each other from the increased positive charge of the nucleus, so that the effective nuclear charge attracting each electron steadily increases through the lanthanoid (lanthanide) elements, resulting in successive reductions of the atomic and ionic radii. The lanthanum ion, La³⁺, has a radius of 1.061 angstroms, whereas the heavier lutetium ion, Lu³⁺, has a radius of 0.850 angstrom. Because the lanthanide contraction keeps these rare-earth ions about the same size and because they all generally exhibit the +3 oxidation state, their chemical properties are very similar, with the result that at least small amounts of each one are usually present in every rare-earth mineral. The lanthanide contraction also is a very significant factor in the extremely close chemical similarity of zirconium (atomic number 40) and hafnium (atomic number 72) of the IVb group of the periodic table. Because of the lanthanide contraction, heavier hafnium, which immediately follows the lanthanoids, possesses a radius nearly identical to the lighter zirconium.