Question

The colour of the \(X_{2}\) molecules of group 17 elements changes gradually from yellow to violet down the group. This is due to [A] the physical state of \(\mathrm{X}_{2}\) at room temperature changes from gas to solid down the group [B] decrease in ionization energy down the group [C] decrease in \(\pi^{*}-\sigma^{*}\) gap down the group [D] decrease in HOMO-LUMO gap down the group

Short answer

The colour of the group 17 element molecules changes from yellow to violet down the group due to a decrease in the HOMO-LUMO gap.

Step-by-step solution

Understand the Trends in Group 17 Elements

Group 17 elements are also known as halogens. The members of this group include Fluorine (F), Chlorine (Cl), Bromine (Br), Iodine (I), and Astatine (At). As we move down the group from F to At, there are observable changes in physical and chemical properties due to the addition of energy levels and the increasing number of electrons.

Analyze the Options

Option [A] suggests a change in physical state could be responsible for the color change. While it's true that the physical state changes from gases (like F2 and Cl2) to liquids (Br2) to solids (I2) down the group at room temperature, this doesn't explain the change in color. Option [B]'s decrease in ionization energy is also observed down the group due to the increasing atomic radius, but this does not directly contribute to the color change. Options [C] and [D] both suggest a decrease in energy gap; however, in the context of color, we are particularly interested in the gap between occupied molecular orbitals (HOMO) and unoccupied molecular orbitals (LUMO). Therefore, we need to consider which energy gap is pertinent to the absorption of light that results in the observed colors.

Determine the Correct Option

The color of molecules can be attributed to the absorption of certain wavelengths of visible light. This absorption corresponds to the energy difference between specific molecular orbitals. For the Group 17 elements, the HOMO-LUMO gap, which represents the energy required to promote an electron from the HOMO (Highest Occupied Molecular Orbital) to the LUMO (Lowest Unoccupied Molecular Orbital), decreases down the group. As a result, the color changes because lower energy (i.e., longer wavelength) light is absorbed as the size of the molecule increases. Thus, the correct answer is option [D] - decrease in HOMO-LUMO gap down the group.

Key concepts

Understanding Group 17 Elements

Group 17 elements, commonly known as halogens, are a fascinating group in the periodic table with distinctive properties. These elements, including Fluorine (F), Chlorine (Cl), Bromine (Br), Iodine (I), and Astatine (At), exhibit a range of colors, and their physical state changes from gases to liquids and eventually to solids down the group at room temperature.

As one moves down this group, the number of electron shells increases, which then influences their reactivity and other chemical behaviors. For example, Fluorine, being the most electronegative element in the group, is a pale yellow gas, while Iodine is a violet solid. This variation is partly because of the different ways electrons absorb and emit light in each element, leading to their unique colors.

The halogens are highly reactive, with reactivity generally decreasing down the group. Fluorine is the most reactive, while Astatine is the least reactive. Their high reactivity is due to their electron configuration; they all have seven electrons in their outermost shell, making them one electron short of a complete octet. This strong desire to fulfill the octet rule drives their behaviors in chemical reactions, such as bond formation with metals to create salts.

The Role of HOMO-LUMO Gap in Color Changes

The HOMO-LUMO gap plays a key role in the color you observe in halogen molecules. 'HOMO' stands for 'Highest Occupied Molecular Orbital,' which contains the outermost electrons in a molecule. 'LUMO,' on the other hand, means 'Lowest Unoccupied Molecular Orbital,' and it is here that an electron can be excited to.

When you think about group 17 elements, the color changes down the group due to the decrease in the energy gap, known as the HOMO-LUMO gap. In simpler terms, as the electrons jump from a lower energy level (HOMO) to a higher energy level (LUMO), they absorb light in the process. If the energy gap is smaller, less energy (or longer wavelengths of light) is needed for this jump. Consequently, the absorbed light corresponds to the different colors observed in halogen molecules as the gap narrows down the group.

This concept explains the variation in color from Fluorine to Astatine – as the molecules increase in size, their electrons have more room to spread out, which lowers the energy needed for electronic transitions, and hence, colors shift from the violet end of the spectrum towards the red end as the HOMO-LUMO gap decreases.

Molecular Orbital Theory and Electron Transitions

Molecular Orbital Theory provides an advanced framework for understanding how electrons are arranged in molecules and how they interact with light to give substances their color. According to this theory, electrons in a molecule are not confined to individual atoms but are distributed over the entire molecule in what are called molecular orbitals.

Molecular orbitals form when atomic orbitals of the bonding atoms combine. There are different kinds of molecular orbitals, such as bonding orbitals, which are lower in energy and anti-bonding orbitals, which are higher in energy. The HOMO is typically a bonding orbital, while the LUMO can be an anti-bonding orbital.

Electrons transition from the HOMO to the LUMO when they absorb energy, say from light. The specific wavelength of light absorbed depends on the energy difference between these two orbitals. This process is central to the concept of electronic transitions and is critical in explaining the observed color changes in halogen molecules. By providing an electron with enough energy to jump from an occupied to an unoccupied orbital, we are able to witness the beautiful palette of colors, from yellow to violet, displayed by the group 17 elements.