Which one of the following ions is colourless in its aqueous solution? (a) \(\mathrm{T}_{1}^{3+}\) (b) \(\mathrm{Cu}^{2+}\) (c) \(\mathrm{Ni}^{2+}\) (d) \(\mathrm{Zn}^{2+}\)

Transition metals are known for their vibrant colors in compounds, particularly when dissolved in water. This colorful display is not mere coincidence but the result of a process called d-orbital electronic transitions. In the d-orbitals of transition metal ions, electrons exist in an array of energy levels. When light hits these ions, electrons can absorb energy and 'jump' to a higher energy d-orbital. This energy corresponds to the energy of a particular color of light.

The energy difference between d-orbitals in a transition metal ion varies, and so does the particular color absorbed. The remaining light, which is not absorbed, then combines to yield the color we perceive. For instance, if an ion absorbs red light, the complementary color green is what we see. Transition metals' unfilled d-orbitals allow for these transitions, which is why a fully filled or empty d-orbital would preclude such color manifestations.

The existence of unpaired electrons in transition metals is a deciding factor for their chemical and physical properties, including magnetism and the ability to form colored compounds. Unpaired electrons are those that do not have an opposing electron sharing the same orbital. In the context of transition metals, the focus falls on the d-orbitals.

Unpaired electrons are prone to align with magnetic fields, making substances that contain such electrons magnetic. This magnetism is why iron, with its unpaired d-electrons, is so strongly attracted to magnets. In terms of color, these unpaired electrons absorb and emit light, creating the vivid colors associated with transition metal solutions. For example, the deep blue of a copper sulfate solution comes from unpaired electrons in the copper ion absorbing energy and releasing it as that characteristic hue. A transition metal ion without unpaired electrons, such as a fully filled or empty d-orbital, will not exhibit color and will not interact with magnetic fields in the same way.

When transition metals are dissolved in water, they form aqueous solutions that often exhibit colors due to the various electronic transitions discussed earlier. The interaction of water molecules with the transition metal ions can even alter the energies of the d-orbitals, and hence, the color can change depending on the specific ligands attached to the metal ion. For example, the color of hydrated copper(II) ions in solution is distinctly different from the color when copper(II) forms complex ions with other ligands such as ammonia.

In an aqueous solution, the surrounding water molecules act as ligands, bonding to the transition metal ion. These interactions can split the d-orbitals into different energy levels, a phenomenon termed crystal field splitting. The specific pattern and intensity of colors observed are a result of both the nature of the metal ion itself and its interaction with the surrounding water molecules. Interestingly, changes in pH, ligand concentration, or the presence of other ions can induce further color changes as they alter the electronic environment of the metal ion.