The differences in zero-point energy between isotopes

[Chaste]

Hi all,

May I know which would have a higher vibrational energy at ground state, zero point energy, maximum vibrational quantum number, between the these 2 isotopes: H₂ and D₂

and why?

 

[kanato]

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 D₂ will have a lower oscillation frequency due to the larger mass.

 

[Chaste]

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 D₂ will have a lower oscillation frequency due to the larger mass.

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 v_max and v_eq. so there shd be no change as well?

 

[Chaste]

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 v_max . so there shd be no change as well?

and for v_eq it should be affected as it's related to the oscillation frequency as well.