Proceedings of the Royal Society of London Series A Containing Papers of a Mathematical and Physical Character · 1927 · 150 citations · 0 references
Natural SciencesChemistryPhysicsNuclear PhysicsPhysical ChemistryQuantum ChemistryHydrogen AtomMolecular SymmetryNuclear StructureRotational StructureMolecular Rotational StatesRotational Level PopulationsRotational LevelsRotational Quantum StatesSpecific Heat Capacity
Hund treated the specific heat of H₂ using wave mechanics, noting that rotational states split into symmetric and antisymmetric groups due to the molecule’s homopolar character. Assuming nuclear spin, Hund derived a rotational specific‑heat expression where weak transitions between symmetric and antisymmetric states are governed by a coupling parameter β, the ratio of their statistical weights. Experimental agreement is achieved when β≈2, implying symmetric states are twice as numerous, which yields a moment of inertia I = 1.54 × 10⁻⁴¹ g cm². The moment of inertia is expressed in cm units.
In a recent article F. Hund has treated the problem of the specific heat of the hydrogen molecule on the basis of the wave mechanics. The total number of rotational states are divided due to the homopolar character of the molecule into two groups, to the one of which belong wave functions symmetrical in the two nuclei, and to the other wave functions which are antisymmetrical in the nuclei. Hund has suggested that the presence of both groups in hydrogen may be accounted for by assuming that the nuclei possess a spin, in which case transitions between symmetrical or between antisymmetrical states will have their usual intensity but transitions between symmetrical and antisymmetrical states will be very weak, of the order of the coupling of the nuclear spins. He then writes the following expression for the rotational specific heat, C r /R = σ 2 d 2 / d σ 2 log Q, Q = β [1 + 5 e -6σ + 9 e -20σ + ...] + 3 e -2σ + 7 e -12σ + 11 e -30σ +...., (1) where σ = h 2 /8π 2 I k T and β is the ratio of the weights of the symmetrical group of states to the antisymmetrical group. Hund has found that he obtains a close agreement between (1) and the observed specific heat curve only when β has about the value 2, that is when the symmetrical states have twice the weight of the antisymmetrical. He further obtains for this case I = 1·54 × 10 -41 gm. cm. 2 , the moment of inertia of the H 2 molecule.