For each of the following complexes, draw a crystal field energy-level diagram, assign the electrons to orbitals, and predict the number of unpaired electrons. 
(d) [Cu(en)2]2+ (square planar) 

Verified step by step guidance

1. Identify the metal ion and its oxidation state. Copper in [Cu(en)_2]^{2+} is in the +2 oxidation state, so it is Cu^{2+}.
2. Determine the electron configuration of the Cu^{2+} ion. Copper has an atomic number of 29, so its electron configuration is [Ar] 3d^{10} 4s^1. For Cu^{2+}, remove two electrons, resulting in [Ar] 3d^9.
3. Recognize that the complex is square planar, which typically involves dsp^2 hybridization. In square planar complexes, the d_{x^2-y^2} orbital is the highest in energy.
4. Draw the crystal field splitting diagram for a square planar complex. The order of energy levels from highest to lowest is: d_{x^2-y^2}, d_{xy}, d_{z^2}, d_{xz}, d_{yz}.
5. Assign the 9 d-electrons of Cu^{2+} to the orbitals in the crystal field diagram, starting from the lowest energy level. Predict the number of unpaired electrons based on the electron configuration.

Key Concepts

Crystal Field Theory

Crystal Field Theory (CFT) explains how the arrangement of ligands around a central metal ion affects the energy levels of its d-orbitals. In octahedral or square planar complexes, the d-orbitals split into different energy levels due to the electrostatic interactions between the ligands and the d-electrons. Understanding this splitting is crucial for predicting the electronic configuration and magnetic properties of the complex.

Electron Configuration

Electron configuration refers to the distribution of electrons in an atom's orbitals. For transition metals, this involves filling the d-orbitals according to the Aufbau principle, Hund's rule, and the Pauli exclusion principle. In the case of [Cu(en)2]2+, knowing the electron configuration of copper and how it changes upon complex formation is essential for determining the number of unpaired electrons.

Unpaired Electrons and Magnetism

Unpaired electrons are electrons that occupy an orbital alone rather than in pairs. The presence of unpaired electrons in a complex contributes to its magnetic properties; complexes with unpaired electrons are paramagnetic, while those with all paired electrons are diamagnetic. Identifying the number of unpaired electrons in [Cu(en)2]2+ helps predict its magnetic behavior and is a key aspect of understanding its chemical properties.