Problem 32 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

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 [Adv. 2017] (a) The physical state of \(X_{2}\) 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

Step-by-Step Solution

Answer

(d) Decrease in HOMO-LUMO gap down the group.

Step 1: Understand the Question

We need to figure out why the color of diatomic molecules \(X_2\) of group 17 elements changes from yellow to violet as you move down the periodic table.

Step 2: Analyze Each Option

There are four given options: (a) Physical state changes from gas to solid, (b) Decrease in ionization energy, (c) Decrease in \(\pi^{*}-\sigma^{*}\) gap, (d) Decrease in HOMO-LUMO gap.

Step 3: Evaluate Color Change Causes

Color changes in molecules are often due to electronic transitions. The most relevant cause could be the change in energy gaps between molecular orbitals.

Step 4: Eliminate Irrelevant Options

Options (a) and (b) do not directly relate to electronic transitions impacting color. They relate to physical properties and ionization energy but not to color.

Step 5: Consider Electronic Transition Gaps

Both (c) and (d) concern molecular orbital gaps: \(\pi^{*}-\sigma^{*}\) gap and HOMO-LUMO gap. The color change is typically due to the HOMO-LUMO gap affecting light absorption.

Step 6: Choose the Correct Option

The color change from yellow to violet is due to the *decrease in the HOMO-LUMO gap* down the group because this influences the wavelength of light absorbed.

Key Concepts

Color Change in Molecules

Color changes in molecules, especially in the context of diatomic molecules like those in Group 17, are a fascinating phenomenon. These changes happen because of alterations in how molecules absorb light. When light hits a molecule, it excites electrons, which then jump between energy levels within the molecule. The specific energy levels involved determine what color we perceive. This is because each color of light has a specific energy associated with it. Thus, as energy levels change, so do the colors we observe in molecules.

• Yellow light is relatively low in energy.
• Violet light, on the other hand, is high in energy.

This transition happens as we move down the group from fluorine, which is yellow, to iodine, which is violet. The decreasing HOMO-LUMO gap, which we will discuss soon, plays a key role in this color change. As a result, the molecules absorb and subsequently reflect different wavelengths of light, causing the observed color changes.

HOMO-LUMO Gap

The HOMO-LUMO gap is a critical concept in understanding why molecular colors change. HOMO stands for "Highest Occupied Molecular Orbital," and LUMO stands for "Lowest Unoccupied Molecular Orbital." The energy difference between HOMO and LUMO dictates what portion of the light spectrum a molecule can absorb. If this gap is large, molecules absorb light from the higher energy (violet) end of the spectrum and appear as colors from the opposite end (like red or yellow).

As the HOMO-LUMO gap decreases, molecules can absorb longer wavelengths of light, which are lower in energy. This causes a shift towards absorbing light from the lower energy (red to yellow) end, thereby reflecting higher energy colors like blue or violet up the group.

• Large HOMO-LUMO gap: absorb high energy, appear low energy colors.
• Small HOMO-LUMO gap: absorb low energy, appear high energy colors.

Thus, the gradual decrease in the HOMO-LUMO gap from top to bottom in Group 17 elements contributes directly to the shift in visible color.

Periodic Table Trends

Understanding periodic trends can help predict the properties of elements, including their behavior regarding color changes. Group 17 consists of halogens, which become heavier and larger as one moves down the group from fluorine to iodine. This change in size and weight influences many aspects of the elements, including the HOMO-LUMO gap.

As we descend the group:

• The atomic size increases due to the addition of more electron shells leading to greater energy levels within the atom.
• This results in a reduction in the energy difference between HOMO and LUMO, or the HOMO-LUMO gap.
• This decreasing gap changes the wavelength of light that the molecules absorb, and consequently alters the color.

This trend is not only relevant to understanding color shift but also helps predict many other chemical and physical properties of the elements within other groups of the periodic table. Hence, paying attention to periodic trends provides a foundational understanding of such transformations.