Question

The isotope effect says that the critical temperature for the superconductivity decreases as the mass of the positive ions increases. Can you argue why it should decrease?

Short answer

For positive ions with a higher mass, the vibration frequency required is lower, and thus the energy of the photons will be lower and temperature is lower.

Step-by-step solution

Significance of isotope

Isotope effects, which result from zero-point fluctuations, manifest the quantum nature of nuclei; they cause variations in the vibrationally averaged properties of compounds containing the lesser and heavier hydrogen isotopes.

Step 2:

Cooper pairs in a superconductor are in ordered state where they all share the same momentum. This ordered state has a lower energy than that of normal state.

Step 3:

The critical temperature of a superconductor is when the energy of the collision between the electron and the lattice is large enough to break the cooper pairs apart.

Therefore, as mass of the positive ions increases temperature decreases.