Explanation:

Ion exchange is a popular method for separating and purifying lanthanides. The method is based on the principle of exchanging ions between a solid resin and a solution containing the lanthanide ions. The resin contains functional groups that can attract and retain specific ions from the solution. The separation of lanthanides is based on the difference in the size of their hydrated ions.

Size of the hydrated ions:

Lanthanides have similar chemical properties due to their electronic configuration, but their ionic radii differ due to the lanthanide contraction. The lanthanide contraction is the decrease in the size of the ionic radii of the lanthanides as the atomic number increases. The decrease in the size of the ionic radii is due to the increasing number of protons in the nucleus, which attracts the outermost electrons more strongly, leading to a contraction of the electron cloud.

The size of the hydrated ions of lanthanides depends on their ionic radii and the number of water molecules attached to them. The ionic radii of lanthanides decrease from La to Lu, whereas the number of water molecules attached to the ions increases with increasing atomic number, due to an increase in the charge density of the ions.

Ion exchange method:

In the ion exchange method, a resin containing functional groups that can attract and retain ions from a solution is used. The functional groups may be negatively charged, positively charged, or neutral. The resin is in the form of small beads, which are packed into a column. The solution containing the lanthanide ions is passed through the column, and the ions are attracted to and retained by the functional groups on the resin.

The retention of the lanthanide ions by the resin depends on the size of the hydrated ions. The larger the hydrated ion, the more strongly it is attracted to and retained by the functional groups on the resin. Therefore, the lanthanides are separated based on the difference in the size of their hydrated ions.

Conclusion:

In conclusion, the separation of lanthanides in ion exchange method is based on the difference in the size of their hydrated ions. The larger the hydrated ion, the more strongly it is attracted to and retained by the functional groups on the resin. Therefore, the method is useful for separating lanthanides with similar chemical properties but different ionic radii.