JEE Challenger
More from p-Block Elements (Group 15-18)
ChemMedAdv 2017 • Paper 1

Gradual Color Change of Group 17 Halogen Molecules Down the Group

For group 17 elements, the color of X2\text{X}_2 molecules deepens gradually from yellow to violet moving down the group. This phenomenon occurs because of:

Options

A

the physical state of X2\text{X}_2 at room temperature shifting from gaseous to solid down the group

B

a decrease in ionization energy going down the group

C

a decrease in the π∗−σ∗\pi^* - \sigma^* energy gap down the group

Correct
D

a decrease in the HOMO-LUMO gap going down the group

Correct

Topics & Concepts

p-Block Elements (Group 15-18)p-Block ElementsPeriodic Trends

Step-by-Step Solution

The color of halogen molecules (X2\text{X}_2) arises from the absorption of visible light, which promotes an electron from a occupied molecular orbital to an unoccupied molecular orbital.

  1. Molecular Orbital (MO) Configuration of X2\text{X}_2: The valence electron configuration for a homonuclear diatomic halogen molecule (X2\text{X}_2, where X=F, Cl, Br, I\text{X} = \text{F, Cl, Br, I}) is: σ(ns)2  σ∗(ns)2  σ(npz)2  π(npx)2  π(npy)2  π∗(npx)2  π∗(npy)2  σ∗(npz)0\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

    • Highest Occupied Molecular Orbital (HOMO): Antibonding π∗\pi^* orbitals (πnp∗\pi^*_{np})
    • Lowest Unoccupied Molecular Orbital (LUMO): Antibonding σ∗\sigma^* orbital (σnp∗\sigma^*_{np})

  2. Electronic Transition and Energy Gap: Absorption of light causes an excitation of an electron from the HOMO (π∗\pi^*) to the LUMO (σ∗\sigma^*). Thus, the energy required for this electronic transition is equal to the energy difference between these orbitals: ΔE=ELUMO−EHOMO=E(σ∗)−E(π∗)\Delta E = E_{\text{LUMO}} - E_{\text{HOMO}} = E(\sigma^*) - E(\pi^*)

  3. Trend Down Group 17:

    • As we move down the group from F2\text{F}_2 to I2\text{I}_2, the principal quantum number nn increases, leading to larger and more diffuse atomic pp-orbitals.
    • The overlap between these larger atomic orbitals decreases, which reduces the energy separation between the molecular orbitals.
    • Consequently, both the π∗−σ∗\pi^* - \sigma^* energy gap and the HOMO-LUMO gap decrease down the group: ΔE(F2)>ΔE(Cl2)>ΔE(Br2)>ΔE(I2)\Delta E(\text{F}_2) > \Delta E(\text{Cl}_2) > \Delta E(\text{Br}_2) > \Delta E(\text{I}_2)

  4. Effect on Transmitted Color: Since ΔE=hcλ\Delta E = \frac{hc}{\lambda}, a smaller energy gap (ΔE\Delta E) requires light of lower energy (longer wavelength, λ\lambda) for excitation:

    • F2\text{F}_2 absorbs high-energy UV/violet light   ⟹  \implies appears light yellow.
    • Cl2\text{Cl}_2 absorbs blue light   ⟹  \implies appears greenish-yellow.
    • Br2\text{Br}_2 absorbs green light   ⟹  \implies appears reddish-brown.
    • I2\text{I}_2 absorbs yellow light   ⟹  \implies appears deep violet.

Therefore, the gradual deepening of color down the group is due to a decrease in the π∗−σ∗\pi^* - \sigma^* gap as well as a decrease in the HOMO-LUMO gap.

Correct Options: [C] decrease in π∗−σ∗\pi^* - \sigma^* gap down the group [D] decrease in HOMO-LUMO gap down the group

PreviousNext