The discussion centers on the differences in zero-point energy between the isotopes H2 and D2, specifically focusing on their vibrational energy at ground state, maximum vibrational quantum number, and equilibrium vibrational energy. The scope includes theoretical considerations of vibrational frequencies and quantum mechanics.
Participants express differing views on the implications of mass on maximum vibrational quantum number and equilibrium vibrational energy, indicating that the discussion remains unresolved regarding these relationships.
Participants have not reached a consensus on how mass influences maximum vibrational quantum number and equilibrium vibrational energy, and there are unresolved assumptions regarding the relationships between these quantities.
kanato said:The zero point energy is proportionate to the frequency of oscillation, and in the typical model system of masses connected by a spring, the oscillation frequency goes as \sqrt{k/m}. The spring constant k is determined by the chemistry and will be unaffected by the nuclear masses. So D<sub>2</sub> will have a lower oscillation frequency due to the larger mass.
Chaste said:thanks.
so what about it's maximum vibrational quantum number and it's equilibrium vibrational energy? are they the same? but thinking about ur statement, there's no mass to consider when relating to vmax . so there shd be no change as well?