Compounds of copper(II) are generally colored, but compounds of copper(I) are not. Explain. Would you expect \(\mathrm{Cd}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}_{2}\) to be colored? Explain.

Copper compounds exhibit a wide range of colors, which has fascinated chemists and artists alike. Copper exists mainly in two oxidation states in its compounds: copper(I) with a +1 charge and copper(II) with a +2 charge. Copper(I) compounds, such as copper(I) chloride (CuCl), are usually white or colorless because their electrons are arranged in a way that doesn't allow them to absorb visible light. In contrast, copper(II) compounds, like copper(II) sulfate (CuSO₄), are often blue or green. This difference in color is directly related to the electronic configuration of the copper ions within these compounds.

To understand this better, let's look at the electronic structure of neutral copper. It has 29 electrons, with the outermost configuration being [Ar] 4s1 3d10. Upon losing an electron to form copper(I), it achieves a full d subshell ([Ar] 3d10), which is more stable and does not easily allow for the transition of electrons between energy levels that would cause color. However, copper(II) ions, with one electron less ([Ar] 3d9), have an unpaired electron which facilitates the absorption of light and subsequent color changes.

The electronic configuration of atoms is akin to the distribution of seats in a theater. Just as theater seats are filled following certain rules, electrons occupy orbitals around the nucleus of an atom in a specific manner. For elements, this configuration follows the principles set out by the rules of quantum mechanics. Outer electrons, particularly those in the d and f orbitals, greatly influence the chemical behavior and properties of the element, including color when it forms compounds.

The electronic configuration of copper, for example, starts with all its electrons nicely arranged in their seats; when it loses one electron to become copper(I), it retains a full d subshell. For copper(II), losing one more electron leaves an open seat in the 3d subshell – a scenario ripe for electron transitions that can give us a visual feast of color.

Think of the d orbitals as a set of five boxes where electrons can be placed. In the case of transition metals like copper, electrons in the d orbitals are the ones responsible for many of their interesting and diverse properties, including color. When copper becomes a copper(I) ion, it has its d orbital boxes completely filled with electrons, thus there is no room for an electron to jump to a higher energy level within the d orbitals.

However, in copper(II) ions, one of these boxes is not entirely full – there is room for an electron to get excited and move to a higher level. These movements, or transitions, absorb certain wavelengths of light, and the wavelengths that are not absorbed are reflected back to our eyes, which we perceive as the compound's color. D orbital electrons are like skilled dancers, where their movements choreograph the vibrancy we observe.

The concept of light absorption and electron excitation is very much like a dance floor where electrons are dancers that can step up to higher energy levels when they 'hear' the right 'tune' of light. When a photon of visible light with the correct energy hits an electron, it can absorb this energy and move to a higher energy orbital. This is known as electron excitation.

In copper(II) compounds, the unpaired d orbital electron can be excited by visible light leading to color. Conversely, in copper(I) and cadmium(II) compounds where there are no unpaired d electrons, there is no 'dance' because there are no available higher energy states in the same energy range as visible light, thus they don't absorb visible light and remain colorless to our eyes. The details of light absorption and the resulting color are determined by the specific electronic configuration of the metal ions involved.