HardChemistryHigh School (11–12)The d- and f-Block Elements › Lanthanoids and Actinoids (f-Block)Numerical

The ion Y³⁺ has a radius of 90.0 pm. The radii of the 3+ ions of the heavy lanthanoids are: Gd…

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The ion $\text{Y}^{3+}$ has a radius of $90.0\ \text{pm}$ . The radii of the 3+ ions of the heavy lanthanoids are: Gd $93.8$ , Tb $92.3$ , Dy $91.2$ , Ho $90.1$ , Er $89.0$ , Tm $88.0$ , Yb $86.8$ and Lu $86.1\ \text{pm}$ . Find the lanthanoid whose ion is closest in size to $\text{Y}^{3+}$ , its atomic number, and the difference in radius.

Need a reminder? The key ideaShow

Going down a group adds a shell, and the radius rises. Between La and Hf, 14 electrons enter the 4f subshell, which shields badly. The effective charge on the outer electrons rises by about $0.15$ at each step, and the ions shrink: $r \approx r_0 \times \dfrac{Z_{eff,0}}{Z_{eff}}$ . The ionic potential is charge divided by radius. A larger value means a stronger pull on $\text{OH}^-$ and a weaker base.

The worked solution

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