Tunneling through energy barriers is a purely quantum-mechanical effect. It is explained by the fact — Physical Chemistry Chemistry Question
Tunneling in chemistry
Tunneling through energy barriers is a purely quantum-mechanical effect. It is explained by the fact that wave functions can differ from zero even in the classically forbidden areas where energy of a particle is less than an energy barrier:
[VISUAL]
Inversion of ammonia is a widely known example of tunneling:
[VISUAL]
In this process the molecule of ammonia is turned out like an umbrella against a strong wind. The tunneling frequency is 24 GHz, and the energy barrier separating two states is 25 kJ mol–1.
Draw the reaction energy profile (plot of energy vs. reaction coordinate) for the inversion of ammonia. What is the reaction coordinate? What coordinate corresponds to the maximum of energy?
Model Answer
Energy profile is the symmetric double-well curve, where the minima correspond to stable pyramidal geometries of ammonia and the maximum – to the unstable planar geometry.
[VISUAL]
The reaction coordinate is the bond angle ∠HNH. In the planar geometry corresponding to the maximum of energy ∠HNH = 120o.
In which region of the electromagnetic spectrum can the tunneling of ammonia be observed?
Model Answer
The wavelength for the tunneling transition is
λ = c / ν = 3.00 × 10^10 cm s^–1 / (24 × 10^9 s^–1) = 1.25 cm.
This wavelength corresponds to radiowaves.
Find the energy difference corresponding to the tunneling frequency. What is the ratio of this energy to the barrier height?
Model Answer
The transition energy per 1 mol is:
ΔE = h * ν * N_A = 6.63 × 10^–34 J s * 24 × 10^9 s^–1 * 6.02 × 10^23 mol^–1 = 10 J mol^–1,
which accounts for 10 / 25000 = 0.0004, or 0.040 % of the energy barrier.
How would the tunneling frequency change if we substitute some hydrogen atoms by deuterium ones? Explain.
Model Answer
Tunneling of the heavier particles is less probable, hence the tunneling frequency for deuterated ammonia is smaller than that for NH3.