分子 Molecular Spectroscopy · Laboratory experiment

Electronic absorption spectrum of iodine vapour: dissociation energy

Aim: to record the B ³Π0u+ ← X ¹Σg+ absorption band system of I₂, assign the vibrational progressions, construct a Birge–Sponer plot, locate the convergence limit, and determine the dissociation energies D₀′ (B state) and D₀″ (ground state).

Absorption spectrometer

Transmission spectrum of the iodine cell

Each dip is the violet-side band head of a v′ ← v″ band. Click a band to mark it. Drag to zoom (the bands crowd together toward 500 nm); double-click to reset.

Observation table

For the convergence limit, enter "conv" as v′

Birge–Sponer plot (v″ = 0 progression)

Results

Theory

A band v′ ← v″ lies at

$$ \tilde\nu(v',v'') = T_e + G'(v') - G''(v''),\qquad G(v) = \omega_e(v+\tfrac12) - \omega_ex_e(v+\tfrac12)^2 + \dots $$

For a progression from v″ = 0, the spacing between successive bands is the vibrational quantum of the upper state:

$$ \Delta G'(v'+\tfrac12) = \tilde\nu(v'+1,0)-\tilde\nu(v',0) = \omega_e' - 2\omega_e'x_e'(v'+1) .$$

The spacing shrinks as the molecule nears dissociation. Plotting ΔG against (v′+1) and extrapolating to zero is the Birge–Sponer method. The area under the line is the dissociation energy of the B state measured from v′ = 0:

$$ D_0' = \sum_{v'} \Delta G'(v'+\tfrac12) \approx \frac{\omega_e'^2}{4\omega_e'x_e'} .$$

Above the convergence limit the spectrum turns into a continuum: the molecule dissociates into I(²P₃/₂) + I*(²P₁/₂). Energy conservation then gives the ground-state dissociation energy:

$$ \tilde\nu_{conv} = D_0'' + E(\mathrm I^*) \;\Rightarrow\; D_0'' = \tilde\nu_{conv} - 7603\ \text{cm}^{-1} .$$

Accepted values: \(\tilde\nu_{conv}\) ≈ 20 043 cm⁻¹ (≈ 499 nm), \(D_0''\) = 12 440 cm⁻¹ = 1.542 eV, \(\omega_e'\) = 125.7 cm⁻¹, \(\omega_e''\) = 214.5 cm⁻¹.

Procedure

  1. Warm the cell (40–60 °C) so the vapour pressure gives a peak absorbance of about 0.5–1.
  2. Record the spectrum from 490 to 650 nm with a narrow slit.
  3. Identify the v″ = 0 progression (the stronger bands below about 560 nm) and assign v′. Hot bands from v″ = 1 lie 213 cm⁻¹ lower and become stronger as the cell is heated.
  4. Convert each λ (air) to ν̃ (vacuum), compute ΔG′ for successive bands, and make the Birge–Sponer plot.
  5. Mark the onset of the continuum (convergence limit) directly as well, and compare it with the extrapolation.

Notes on the model

The X- and B-state constants are from Huber & Herzberg. The B-state vibrational ladder includes a cubic anharmonic term, so the Birge–Sponer plot curves downward near dissociation, as it does for real I₂. A linear extrapolation from low v′ therefore overestimates D₀′, a well-known limitation of the method. Band intensities follow a Franck–Condon envelope (reflection approximation), the hot-band populations a Boltzmann distribution, and the vapour pressure the Clausius–Clapeyron law.

Viva questions

Why are the bands degraded to the red?

B′ < B″ (the B-state bond is longer), so the R-branch forms a head on the high-wavenumber side and the rotational lines spread toward lower wavenumber.

Why does heating change the spectrum?

Heating raises the vapour pressure (more absorption) and the population of v″ = 1 and 2, so the hot bands at longer wavelength grow.

Why add E(I*)?

The B state correlates with one ground-state and one spin–orbit-excited atom. The convergence limit is therefore D₀″ plus the I* excitation energy.