The colour of the X2 molecules of group 17 elements changes gradually from yellow to violet down the

Q: Why do halogens have color while many other gases like $N_2$ and $O_2$ are colorless?

Halogens have a relatively small HOMO-LUMO energy gap that falls within the visible light spectrum. For molecules like $N_2$, the gap is much larger, requiring high-energy UV light for excitation, making them transparent to visible light.

Q: What exactly are HOMO and LUMO?

HOMO stands for Highest Occupied Molecular Orbital, which is the highest energy level containing electrons. LUMO is the Lowest Unoccupied Molecular Orbital, the first empty level above the HOMO. The transition of an electron between these two dictates the optical properties.

Q: Why does the energy gap decrease down the group?

As you move down the group, the principal quantum number increases, meaning the valence orbitals are larger and more diffuse. This increased size leads to less effective orbital overlap and a smaller energy splitting between the bonding and anti-bonding orbitals, thus narrowing the HOMO-LUMO gap.

Q: If Iodine absorbs yellow light, why does it appear violet?

When a substance absorbs a specific color from white light, our eyes perceive the remaining transmitted or reflected light. Yellow and violet are complementary colors. Absorbing yellow leaves the violet part of the spectrum to reach our eyes.

Q: Does the physical state (gas vs. solid) affect the color?

While the physical state changes down the group due to stronger Van der Waals forces, the fundamental reason for the specific color is the electronic transition within the individual $X_2$ molecules, not the macroscopic physical state.

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 -

Options:

(A) the physical state of $X_2$ at room temperature changes from gas to solid down the group

(B) decrease in HOMO-LUMO gap down the group

(C) decrease in $\pi^*$-$\sigma^*$ down the group

(D) decrease in ionization energy down the group

Sigma Percentile · Accepted Answer

### The Quantum Symphony of Halogen Colors

Have you ever wondered why the halogens are so beautifully colored? If you look at Group 17 of the periodic table, you are greeted with a vibrant palette: Fluorine is a pale yellow gas, Chlorine is greenish-yellow, Bromine is a deep reddish-brown liquid, and Iodine is a striking dark violet solid. This isn't just a random coincidence; it is a direct consequence of quantum mechanics and how molecules interact with visible light.

To understand this, we need to dive into the **Molecular Orbital Theory (MOT)**. The color of any molecule is fundamentally tied to its electrons absorbing light. When visible light hits a halogen molecule, an electron can absorb a photon and jump from a lower energy orbital to a higher energy one.

### Identifying the HOMO and LUMO

But which orbitals are involved? We look at the **Highest Occupied Molecular Orbital (HOMO)** and the **Lowest Unoccupied Molecular Orbital (LUMO)**. For a diatomic halogen molecule $X_2$, the valence shell electronic configuration ends with the anti-bonding pi orbitals being completely filled, and the anti-bonding sigma orbital being completely empty.

Specifically, the configuration is:

$$ \sigma ns^2, \sigma^* ns^2, \sigma np_z^2, \pi np_x^2 = \pi np_y^2, \pi^* np_x^2 = \pi^* np_y^2, \sigma^* np_z^0 $$

Here, the outermost filled orbitals are the $\pi^*$ anti-bonding orbitals. So, they act as our **HOMO**. Just above them lies the empty $\sigma^*$ anti-bonding orbital, which is our **LUMO**. The electronic transition responsible for the color happens right between these two levels: from $\pi^*$ to $\sigma^*$.

### The Trend Down the Group

Now, what happens as we move down the group from Fluorine to Iodine? The principal quantum number increases, meaning the atoms get larger and their valence orbitals become more diffuse. Because the orbitals are larger and further from the nucleus, the energy splitting between the bonding and anti-bonding orbitals becomes less pronounced.

This causes the energy levels to squeeze closer together, significantly **decreasing the HOMO-LUMO gap** ($\Delta E$). Therefore, the energy gap for Fluorine is much larger than the energy gap for Iodine:

$$ \Delta E_{F_2} > \Delta E_{I_2} $$

### Energy, Wavelength, and Complementary Colors

According to the Planck-Einstein relation, the energy of the absorbed photon is inversely proportional to its wavelength:

$$ \Delta E = \frac{hc}{\lambda_{	ext{absorbed}}} $$

Because the energy gap is large for Fluorine, it requires a high-energy photon to excite an electron. It absorbs high-energy **violet light**. When violet is removed from the white light spectrum, our eyes perceive the complementary color, which is **yellow**.

Conversely, Iodine has a much smaller energy gap. It requires less energy to excite an electron, so it absorbs lower-energy **yellow light**. The complementary color that is transmitted and reaches our eyes is **violet**.

This beautiful interplay of atomic size, molecular orbitals, and the visible light spectrum perfectly explains why the color changes from yellow to violet down the group. It is due to the decrease in the HOMO-LUMO gap, which is exactly the gap between the $\pi^*$ and $\sigma^*$ orbitals.

Animated Solution for Chemistry - s and p-Block Elements: The colour of the $X_{2}$ molecules of group 17 elements changes gradually from yellow to violet down the group. This is due to -

Select Answer:

Visualized Solution

\text{Halogen Colours}

\text{Origin of Colour}

\text{HOMO and LUMO of } X_2

\text{Trend Down the Group}

\text{Energy and Wavelength}

\text{Conclusion}

The Sigma Insight: Group 17 Elements

The Quantum Symphony of Halogen Colors

Identifying the HOMO and LUMO

The Trend Down the Group

Energy, Wavelength, and Complementary Colors

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