163.

Use Hund's rule to derive the electronic configuration of Ce³⁺ ion, and calculate its magnetic moment on the basis of 'spin only' formula.

The electronic configuration of Ce and Ce³⁺ ion is :
The electronic configuration of Ce : 1s²2s²2p⁶3s²3p⁶3d¹⁰4s²4p⁶4d¹⁰5s²5p⁶4f¹5d¹6s²
The electronic configuration of Ce3+ : 1s²2s²2p⁶3s²3p⁶3d¹⁰4s²4p⁶4d¹⁰5s²5p⁶4f¹
OR
Ce(Z = 58) = ₅₄[Xe] 4f¹5d¹6s²
Ce³⁺ = ₅₄[Xe] 4f¹

The no. of unpaired electron = 1 ‘Spin only’ formula for magnetic moment of a specie,

                                  $\mathrm{\mu } = \sqrt{\mathrm{n}(\mathrm{n}+2)} \mathrm{B}.\mathrm{M}.$
$$\begin{gathered} \therefore \mathrm{Magnetic} \mathrm{moment} \mathrm{of} {\mathrm{Ce}}^{3+} \\ \mathrm{\mu } = \sqrt{1(1+2)} \mathrm{B}.\mathrm{M}. \\ = \sqrt{3} \mathrm{B}.\mathrm{M}. = 1.732 \mathrm{B}.\mathrm{M}. \end{gathered}$$