# The differences in zero-point energy between isotopes

1. Nov 19, 2009

### 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?

2. Nov 20, 2009

### 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 D<sub>2</sub> will have a lower oscillation frequency due to the larger mass.

3. Nov 20, 2009

### 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 vmax and veq. so there shd be no change as well?

4. Nov 20, 2009

### Chaste

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