The aqueous solution containing which one of the following ions will be colourless? (a) \(\mathrm{Sc}^{3+}\) (b) \(\mathrm{Fe}^{3+}\) (c) \(\mathrm{Fe}^{2+}\) (d) \(\mathrm{Mn}^{2+}\)

When it comes to the enchanting world of colorful solutions, transition metal ions are the star performers. The variety of colors we observe in aqueous solutions of these ions is due to the presence of d-orbitals, which are unique to transition elements. These d-orbitals allow for a fascinating phenomenon known as 'd-d transitions.' If we take a closer look, we can see that ions with incompletely filled d-orbitals usually exhibit colors in solution. Imagine an artist's palette, but instead of paints, we're dabbing with electrons!

For instance, the copper(II) ion (Cu^{2+}) adds a beautiful blue hue to its solution. It's all about what’s happening on a microscopic scale – electrons leaping between energy levels. However, not all transition metals show color. Scandium ions (Sc^{3+}), with their d-orbitals empty (d0), lack the ability to absorb visible light to promote electrons and, therefore, are like invisible ink – colorless in solution.

Electronic configurations are like the personal ID of an atom, telling us how its electrons are arranged. These configurations follow a specific order and can sometimes appear as complex as a social security number. Transition metals, with their d-orbitals, have electronic configurations that directly influence their chemical behavior and properties. In the context of our color conundrum, knowing whether a transition metal ion has an electronic configuration of d0 or d10 is crucial.

An ion with d0 means all available seats in the d-orbital are empty, think of it as a concert hall before the audience arrives – not much is happening. Likewise, a d10 configuration means the d-orbital is at full capacity, like a packed stadium during the finale of a concert – no room for any more action. These 'quiet' or 'full house' scenarios result in the aqueous ions being colorless, as there's no room for electrons to move to higher energy states.

Descending into the world of d-orbital electronic transitions is like diving into a sea of intricate dances between light and electrons. In transition metal ions, electrons can get excited and jump between different levels within the d-orbitals. These transitions aren't random; they need just the right amount of energy, typically from visible light, to make the leap.

As light hits an aqueous solution, certain wavelengths are absorbed by these electrons as they jump up to higher energy states. Once the light is absorbed, the remaining light – which we see – is missing those wavelengths, giving us the perceived color of the solution. Think of it as a spectral selective filter: certain wavelengths go in, some are trapped, and the remaining spectrum that passes through 'paints' the solution with color. If there's no place for an electron to jump to – as with a d0 or d10 configuration – the solution will stay colorless. This makes d-orbital electronic transitions the nucleus of understanding why we see the vivid spectrum of colors in transition metal ion solutions.